Consumer price inflation trends

Imports #

Only the standard Python data science packages and the specialized macrosynergy package are needed. 

import os
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np

import macrosynergy.management as msm
import macrosynergy.panel as msp
import macrosynergy.signal as mss
import macrosynergy.pnl as msn

from macrosynergy.download import JPMaQSDownload

import warnings
warnings.simplefilter("ignore")

The JPMaQS indicators we consider are downloaded using the J.P. Morgan Dataquery API interface within the macrosynergy package. This is done by specifying ticker strings , formed by appending an indicator category code <category> to a currency area code <cross_section> . These constitute the main part of a full quantamental indicator ticker, taking the form DB(JPMAQS,<cross_section>_<category>,<info>) , where <info> denotes the time series of information for the given cross-section and category. The following types of information are available:

  • value giving the latest available values for the indicator

  • eop_lag referring to days elapsed since the end of the observation period

  • mop_lag referring to the number of days elapsed since the mean observation period

  • grade denoting a grade of the observation, giving a metric of real time information quality.

After instantiating the JPMaQSDownload class within the macrosynergy.download module, one can use the download(tickers,start_date,metrics) method to easily download the necessary data, where tickers is an array of ticker strings, start_date is the first collection date to be considered and metrics is an array comprising the times series information to be downloaded. 

# Cross-sections of interest

cids_dmca = [
    "AUD",
    "CAD",
    "CHF",
    "EUR",
    "GBP",
    "JPY",
    "NOK",
    "NZD",
    "SEK",
    "USD",
]  # DM currency areas
cids_dmec = ["DEM", "ESP", "FRF", "ITL"]  # DM euro area countries

cids_dm = cids_dmca + cids_dmec

cids_em = ["BRL", "COP", "CLP", "MXN", "PEN",  # Latam countries
"CZK", "HUF", "ILS", "PLN", "RON", "RUB", "TRY", "ZAR",  # EMEA countries
"CNY", "IDR", "INR", "KRW", "MYR", "PHP", "SGD", "THB", "TWD"] # Asia countries

cids_early = ["GBP", "JPY", "USD", "RUB", "TRY", "ZAR", "PHP", "SGD"]

cids = sorted(cids_dm + cids_em)

# Quantamental categories of interest

main = [
    "CPIC_SA_P1M1ML12",
    "CPIC_SJA_P1M1ML1",
    "CPIC_SJA_P3M3ML3AR",
    "CPIC_SJA_P6M6ML6AR",
    "CPIC_SA_P1M1ML12_D1M1ML3",
    "CPIH_SA_P1M1ML12",
    "CPIH_SJA_P1M1ML1",
    "CPIH_SJA_P3M3ML3AR",
    "CPIH_SJA_P6M6ML6AR",
    "CPIH_SA_P1M1ML12_D1M1ML3",
]
early = [
    "CPIHE_SA_P1M1ML12",
    "CPIHE_SJA_P3M3ML3AR",
    "CPIHE_SJA_P6M6ML6AR",
    "CPIHE_SA_P1M1ML12_D1M1ML3",
    "CPICE_SA_P1M1ML12",
    "CPICE_SJA_P3M3ML3AR",
    "CPICE_SJA_P6M6ML6AR",
    "CPICE_SA_P1M1ML12_D1M1ML3",
]

misc = ["INFTEFF_NSA", "INFTARGET_NSA"] # Inflation targets 

mark = ["EQXR_NSA",
        "EQXR_VT10", 
        "DU02YXR_VT10", 
        "DU02YXR_NSA", 
        "DU05YXR_VT10", 
        "FXXR_VT10", 
        "GB01YR_NSA", 
        "GB02YR_NSA", 
        "GB03YR_NSA", 
        "GB05YR_NSA",
        "GB01YYLD_NSA"]  # market links

xcats = main + early + mark + misc

# Download series from J.P. Morgan DataQuery by tickers

start_date = "1990-01-01"
tickers = [cid + "_" + xcat for cid in cids for xcat in xcats]
print(f"Maximum number of tickers is {len(tickers)}")

# Retrieve credentials

client_id: str = os.getenv("DQ_CLIENT_ID")
client_secret: str = os.getenv("DQ_CLIENT_SECRET")

with JPMaQSDownload(client_id=client_id, client_secret=client_secret) as dq:
    df = dq.download(
        tickers=tickers,
        start_date=start_date,
        suppress_warning=True,
        metrics=["all"],
        show_progress=True,
    )

Maximum number of tickers is 1116
Downloading data from JPMaQS.
Timestamp UTC:  2024-05-03 09:36:48
Connection successful!

Requesting data: 100%|██████████| 224/224 [00:50<00:00,  4.41it/s]
Downloading data: 100%|██████████| 224/224 [00:21<00:00, 10.51it/s] 

Some expressions are missing from the downloaded data. Check logger output for complete list.
1776 out of 4464 expressions are missing. To download the catalogue of all available expressions and filter the unavailable expressions, set `get_catalogue=True` in the call to `JPMaQSDownload.download()`.
Some dates are missing from the downloaded data. 
2 out of 8962 dates are missing.

Availability # 

cids_exp = sorted(list(set(cids) - set(cids_dmec)))  # cids expected in category panels
msm.missing_in_df(df, xcats=main, cids=cids_exp)
Hide code cell output 
No missing XCATs across DataFrame.
Missing cids for CPIC_SA_P1M1ML12:          []
Missing cids for CPIC_SA_P1M1ML12_D1M1ML3:  []
Missing cids for CPIC_SJA_P1M1ML1:          []
Missing cids for CPIC_SJA_P3M3ML3AR:        []
Missing cids for CPIC_SJA_P6M6ML6AR:        []
Missing cids for CPIH_SA_P1M1ML12:          []
Missing cids for CPIH_SA_P1M1ML12_D1M1ML3:  []
Missing cids for CPIH_SJA_P1M1ML1:          []
Missing cids for CPIH_SJA_P3M3ML3AR:        []
Missing cids for CPIH_SJA_P6M6ML6AR:        []

cids_early = sorted(list(set(cids_early) - set(cids_dmec)))  # cids expected in category panels
msm.missing_in_df(df, xcats=early, cids=cids_early)

No missing XCATs across DataFrame.
Missing cids for CPICE_SA_P1M1ML12:          ['GBP', 'PHP', 'RUB', 'SGD', 'TRY', 'ZAR']
Missing cids for CPICE_SA_P1M1ML12_D1M1ML3:  ['GBP', 'PHP', 'RUB', 'SGD', 'TRY', 'ZAR']
Missing cids for CPICE_SJA_P3M3ML3AR:        ['GBP', 'PHP', 'RUB', 'SGD', 'TRY', 'ZAR']
Missing cids for CPICE_SJA_P6M6ML6AR:        ['GBP', 'PHP', 'RUB', 'SGD', 'TRY', 'ZAR']
Missing cids for CPIHE_SA_P1M1ML12:          ['USD']
Missing cids for CPIHE_SA_P1M1ML12_D1M1ML3:  ['USD']
Missing cids for CPIHE_SJA_P3M3ML3AR:        ['USD']
Missing cids for CPIHE_SJA_P6M6ML6AR:        ['USD']

Real-time quantamental indicators of consumer price inflation trends for developed markets have been typically available by the late 1990s. Data are available, for some emerging markets, from 1990 onwards.

For the explanation of currency symbols related to currency areas or countries for which categories are available, please view Appendix 3 . 

msm.check_availability(
    df,
    xcats=main,
    cids=cids_exp,
    missing_recent=False,
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/eb894872c2924b94dae43425bce3a1f91ce475f74d750395426e944ff8b4b554.png

Only a small subset of countries have CPI inflation indicators based on early indicators. Most of them go back to the 1990s. 

msm.check_availability(
    df,
    xcats=early,
    cids=cids_early,
    missing_recent=False,
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/8ec46fe6818e415b2e0b2655fb34fa1d2bf5a191268901489e08ef1187f2a113.png 
xcatx = main
cidx = cids_exp

plot = msm.check_availability(df, xcats=xcatx, cids=cids_exp, start_years=False)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/7a6b5ac8477937059a1a2a87ff2ca3b2de4efc89c0e7cba994f98e8383e5c506.png 
xcatx = early
cidx = cids_early

plot = msm.check_availability(
    df, xcats=xcatx, cids=cids_exp, start_size=(18, 6), start_years=False
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/54e8348a927171891926f070f9003fa3615a52964362dceeed65f20585a8380b.png

Vintage grading is mixed. USD is the only cross-section that posted the highest average grades back to the 1990s. 

xcatx = main
cidx = cids_exp

plot = msp.heatmap_grades(
    df,
    xcats=xcatx,
    cids=cidx,
    size=(18, 6),
    title=f"Average vintage grades from {start_date} onwards",
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/4e36534fbbafebfad7094dfc3db0925f8e9ee2323307237044411ed927a6e429.png 
xcatx = early
cidx = cids_early

plot = msp.heatmap_grades(
    df,
    xcats=xcatx,
    cids=cidx,
    size=(18, 4),
    title=f"Average vintage grades from {start_date} onwards",
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/4c566fafdffb5f973e7702bb6bdb6a335601a052efe866be4037b9d7af24bbd1.png

The variable eop_lag (or mop_lag ) represents the count of days that have passed since the last (median) of the observation period. Graphing the ranges and timelines of this indicator illustrates the frequency of updates and reveals the fluctuations it has undergone over time. 

xcatx = ["CPIH_SA_P1M1ML12", "CPIC_SA_P1M1ML12"]
cidx = cids_exp

msp.view_ranges(
    df,
    xcats=xcatx,
    cids=cidx,
    val="eop_lag",
    title="End of observation period lags (ranges of time elapsed since end of observation period in days)",
    start=start_date,
    kind="box",
 )
msp.view_ranges(
    df,
    xcats=xcatx,
    cids=cidx,
    val="mop_lag",
    title="Median of observation period lags (ranges of time elapsed since end of observation period in days)",
    start=start_date,
    kind="box",
 
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/bde89aee892bc41aa93185063e692ba1f44c8f5065ade8eb4b414f5fc6042a0b.png https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/11800784fd4d26c07493fe46e23389841e5390c16f506ac9fcf0efda9a6ab296.png 
cidx = ["USD", "EUR", "GBP"]

msp.view_timelines(
    df,
    xcats="CPIC_SA_P1M1ML12",
    cids=cidx,
    val="eop_lag"
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/3ab79b140dfc33c2861a87c9f5e52ab4068bc8aff623e795c3b3b59d221833e4.png 
xcatx = ["CPIHE_SA_P1M1ML12", "CPICE_SA_P1M1ML12"]
cidx = cids_early

msp.view_ranges(
    df,
    xcats=xcatx,
    cids=cidx,
    val="eop_lag",
    title="End of observation period lags (ranges of time elapsed since end of observation period in days)",
    start=start_date,
    kind="box",
    size=(16, 6),
)
msp.view_ranges(
    df,
    xcats=xcatx,
    cids=cidx,
    val="mop_lag",
    title="Median of observation period lags (ranges of time elapsed since end of observation period in days)",
    start=start_date,
    kind="box",
    size=(16, 6),
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/5a49130bf430937febcb6018897c7649217c00d759706daabd07361dee67184b.png https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/f9d536945b73882fac5a65ee2ebfe21da612323574eff86b84805d0814ef3137.png

History #

Annual headline/core consumer price inflation #

Since 2000, headline inflation averages and variances have been materially different across countries. Importantly, there has been a clear linear relation between average inflation and its standard deviation, across currency areas and years. This suggests high inflation comes with high uncertainty. 

xcatx = ["CPIH_SA_P1M1ML12", "CPIC_SA_P1M1ML12"]
cidx = cids_exp

msp.view_ranges(
    df,
    xcats=xcatx,
    cids=cidx,
    sort_cids_by="mean",
    start="2000-01-01",
    kind="bar",
    title="Means and standard deviations of annual CPI measures, seasonally-adjusted, % change over a year ago, since 2000",
    xcat_labels=["Headline", "Core"],
    size=(16, 8),
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/d655e8149f5ecb21d0ff597d4090698e0d2d5267bcf4a6837bc80188ad735fee.png 
dfa = msp.historic_vol(
    df, xcat="CPIH_SA_P1M1ML12", cids=cids, lback_meth="xma", postfix="_ASD"
)
df = msm.update_df(df, dfa)

cr_infl_vol = msp.CategoryRelations(
    df,
    xcats=["CPIH_SA_P1M1ML12", 'CPIH_SA_P1M1ML12_ASD'],
    cids=cids, 
    freq="A",
    lag=0,
    xcat_aggs=["mean", "mean"],
    start="2000-01-01",
   
)

cr_infl_vol.reg_scatter(
    labels=False,
    coef_box="upper left",
    xlab="Headline CPI, seas.-adj., % over a year ago, annual average",
    ylab="Average annualized standard deviation of CPI inflation information states",
    title="Headline inflation and standard deviations of CPI inflation across countries and years since 2000",
    size=(8, 6),
    prob_est="map",
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/1f6bf3f1b84087223d6740a912b2dfceb64391491540dcf08a1d7d818ea68ddb.png

Headline and core inflation can deviate materially, testifying to the power and volatility of food and energy prices. 

cidx = cids_exp
calcs = ["Headline_vs_Core = CPIH_SA_P1M1ML12 - CPIC_SA_P1M1ML12"]
xcatx = ["CPIH_SA_P1M1ML12", "CPIC_SA_P1M1ML12", "Headline_vs_Core"]
dfa = msp.panel_calculator(df, calcs, cids=cids)
df = msm.update_df(df, dfa)


msp.view_timelines(
    df,
    xcats=xcatx,
    cids=cidx,
    start="2000-01-01",
    title="Annual CPI measures, seasonally-adjusted, % change over a year ago",
    title_fontsize=27,
    legend_fontsize=17,
    xcat_labels=["Headline", "Core", "Headline_vs_Core"],
    ncol=4,
    same_y=False,
    all_xticks=True,
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/68219cf15d2122dbfd56a61c5ce801443ce7f2a1e636ba37134a7e34152fd267.png

The basic idea behind core price indices is to exclude volatile or erratic prices that cloud the detection of a trend. Core inflation is seen as more stable measure with lower averages and variabilities for most countries. The difference and variability of this difference varies considerably among cross-sections. “The implicit assumption behind the removal of volatile items from core inflation measures is not only that those price changes are volatile but mainly temporary” IMF Working Paper WP15/8 

calcs = ["Headline_vs_Core = CPIH_SA_P1M1ML12 - CPIC_SA_P1M1ML12"]
dfa = msp.panel_calculator(df, calcs, cids=cids)
df = msm.update_df(df, dfa)

xcatx = ["Headline_vs_Core"]
cidx = cids_exp

msp.view_ranges(
    df,
    xcats=xcatx,
    cids=cidx,
    sort_cids_by="mean",
    start="2000-01-01",
    kind="bar",
    title="Means and standard deviations of Headline and Core Inflation differences, seasonally-adjusted, % change over a year ago, since 2000",
    size=(16, 8),
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/8ae875646775b242c5910cce8c3a21a5ac61b13eea8c6d3f9188cd55d2578b8f.png

The absolute difference between headline and core inflation rates seems to exhibit a positive correlation with the volatility of headline inflation. This relationship strenghened since the Pandemic: 

cr_hvscore_vol = msp.CategoryRelations(
    df,
    xcats=["Headline_vs_Core", 'CPIH_SA_P1M1ML12_ASD'],
    cids=cids, 
    freq="M",
    lag=0,
    xcat_aggs=["mean", "mean"],
    start="2000-01-01",
   
)

cr_hvscore_vol.reg_scatter(
    labels=False,
    coef_box="upper left",
    xlab="Headline and core annual inflation difference, % change over a year ago, since 2000",
    ylab="Headline inflation historic volatility",
    title="Headline-core inflation difference and inflation volatility for all available cross-sections, % change over a year ago, since 2000",
    size=(12, 8),
    prob_est="map",
    separator=2020
    )
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/62cb7027676218833741bcb8ac136b05a7906648c04527c722b164f129fb751e.png

Cross-sectional correlations of headline annual CPI inflation have been predominantly positive since 1990. India and China stand out in displaying the least correlation with other countries. India has a peculiar basket geared towards very low-income earners and used a wholesale price index for the most-watched inflation reports until the 2010s. 

xcatx = "CPIH_SA_P1M1ML12"
cidx = cids_exp

msp.correl_matrix(
    df,
    xcats=xcatx,
    cids=cidx,
    title="Cross-sectional correlations for annual headline CPI trends since 2000",
    start="2000-01-01",
    size=(20, 14),
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/8bf5bf8361006f13940c2e8cced1e3a9d6361d9d497486254ea29a0157fd6ef8.png

Headline inflation correlation has strengthened since 2020 for majority of countries. India and China remained the least correlated. 

xcatx = "CPIH_SA_P1M1ML12"
cidx = cids_exp

msp.correl_matrix(
    df,
    xcats=xcatx,
    cids=cidx,
    title="Cross-sectional correlations for annual headline CPI trends since 2020",
    start="2020-01-01",
    size=(20, 14),
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/98d3708a11d26ba68fd3a156cb510878090da0b6d4679c582dab39565581a265.png

Change in headline consumer price inflation #

Like in inflation trends and variation, also changes in inflation trends (based on concurrent vintages) and their variations have been widely different acrosss countries. 

xcatx = ["CPIH_SA_P1M1ML12_D1M1ML3"]
cidx = cids_exp

msp.view_ranges(
    df,
    xcats=xcatx,
    cids=cidx,
    sort_cids_by="std",
    start="2000-01-01",
    kind="box",
    title="Boxplots for changes in headline consumer price inflation, seasonally-adjusted, since 2000",
    xcat_labels=["3-month difference in 1-year % change"],
    size=(16, 8),
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/582ca24393ed83c985787fc4b9a3b3210dacbd8d5fdf5cffb93a8467bd4990c1.png

The relationship between the current level of inflation and the change in inflation in the next period tends to be negative, suggesting a straightforward concept: high inflation today may prompt actions by policymakers aimed at reducing inflation in the future. 

cr = msp.CategoryRelations(
    df,
    xcats=["CPIH_SA_P1M1ML12", "CPIH_SA_P1M1ML12_D1M1ML3"],
    cids=cids,
    freq="Q",
    lag=1,
    xcat_aggs=["last", "last"],
    xcat_trims=[20,20],
    start="2000-01-01",
)

cr.reg_scatter(
        labels=False,
    coef_box="upper left",
    title = "Annual headline consumer price inflation, versus its change over the past three months, end-of-month information state, since 2000",
    xlab="Standard annual headline consumer price inflation, seasonally adjusted, over the past three months",
    ylab="Next quarter's change in annual headline consumer price inflation over the past three months",
    prob_est="map"
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/7a2d9407d3629f8681270975dd3fb40b89d11781ae566d225d0a53a8d031b3bd.png 
xcatx = ["CPIH_SA_P1M1ML12_D1M1ML3"]
cidx = cids_exp


msp.view_timelines(
    df,
    xcats=xcatx,
    cids=cidx,
    start="2000-01-01",
    title="3-month difference in headline consumer price inflation, % over a year ago, seasonally-adjusted",
    title_fontsize=27,
    ncol=4,
    same_y=False,
    all_xticks=True,
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/d28d761af9612ac062f64906305ee6ff441348abfd72b8d03244bbcaa2a3eb77.png

There has been a dominant positive relation between the information states of headline inflation changes across countries. This means published data across currency areas usually signal the same direction of change. Food and energy prices are main driver of this correlation, but not the only. Also, core inflation changes have been positively correlated. 

xcatx = "CPIH_SA_P1M1ML12_D1M1ML3"
cidx = cids_exp

msp.correl_matrix(
    df,
    xcats=xcatx,
    cids=cidx,
    title="Cross-sectional correlation of headline CPI changes, since 2020",
    start="2020-01-01",
    size=(20, 14),
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/60b405b1f78edd285e6d920cdeee68e5da3c3acc4d97846c6aec81e416e6f87d.png

CPI, using early estimates #

The longer-term pattern of regular CPI inflation and the version with early estimates have naturally been very similar as the two metrics converge on a monthly basis.

For currency areas with regression estimates, such as GBP or PHP, the influence of the early estimate varies over time, in accordance with previous historical experience. This reflects that the predictive regression is sequentially re-estimated in order to avoid any hindsight bias. 

xcatx = ["CPIH_SA_P1M1ML12", "CPIHE_SA_P1M1ML12"]
cidx = msm.common_cids(df, xcats=xcatx)

msp.view_timelines(
    df,
    xcats=xcatx,
    cids=cidx,
    start="2000-01-01",
    title="Headline CPI trends, % change over a year ago, information states",
    legend_fontsize=17,
    xcat_labels=["Regular headline CPI", "Using early estimate prior to release"],
    ncol=4,
    same_y=False,
    all_xticks=True,
    legend_ncol=2,
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/a2b95802e49e98ea259f1c874c1d017feeb30071e95b654213b0272db4397be7.png

Changes in the early headline inflation indicators (%oya over 3 months) are highly accurate in forecasting standard inflation changes (%oya over 3 months), achieving an accuracy rate of approximately 80% across all available countries. 

xcatx = ["CPIH_SA_P1M1ML12_D1M1ML3", "CPIHE_SA_P1M1ML12_D1M1ML3"]
cidx = msm.common_cids(df, xcats=xcatx)

srr = mss.SignalReturnRelations(
    df,
    cids=cids_early,
    sigs=["CPIHE_SA_P1M1ML12_D1M1ML3"],
    sig_neg=[False],
    rets=["CPIH_SA_P1M1ML12_D1M1ML3"],
    freqs=["M"],
    start="2012-01-01",
    end="2023-12-01"
)

srr.accuracy_bars(title = "Accuracy of changes in early headline CPI estimates for all available countries", size = (6,4), title_fontsize = 10)
srr.accuracy_bars(type="years", title = "Accuracy of changes early headline CPI estimates for all available countries", size = (6,4), title_fontsize = 10)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/1cfc140448854fe8b913984eeff358a9409335e866f9e1281e211a5a82457a5f.png https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/c2cf0b74a8792fd4f0e67d99e96fc0d34a6bf588b621caf7f4ec6db80e680177.png

Importance #

Empirical clues #

This section examines the proof of concept, presenting a stylized Profit and Loss (PnL) profile for a collection of trading signals based on inflation. The trading signals involve simple inflation metrics based on excess inflation. Excess inflation pertains to consumer price trends that exceed the predefined inflation target. Our focus in this analysis extends to potential asset classes deemed suitable for consideration:

  • generic government bond returns,

  • directional duration returns,

  • relative duration returns,

  • equity returns,

  • directional FX returns, and

  • relative FX returns. 

# The first step is to calculate the effective inflation target for each country. This is done by taking the maximum of the inflation target and 2%. 

scols=["cid", "xcat", "real_date", "value"]
dfx = df[scols].copy().sort_values(["cid", "xcat", "real_date"])
dfx["ticker"] = dfx["cid"] + "_" + dfx["xcat"]


dfa = msp.panel_calculator(dfx, ["INFTEBASIS = INFTEFF_NSA.clip(lower=2)"], cids=cids) # `INFTEBASIS` is  the maximum of 
# the effective inflation target and 2. 
dfx = msm.update_df(dfx, dfa)

# The second step is to calculate the relative deviations of the inflation rate from the effective inflation target. 

sigx = [
    "CPIH_SA_P1M1ML12",
    "CPIH_SJA_P6M6ML6AR",
    "CPIH_SJA_P3M3ML3AR",
    "CPIC_SA_P1M1ML12",
    "CPIC_SJA_P3M3ML3AR",
    "CPIC_SJA_P6M6ML6AR"
]

for inf in sigx:
    calcs = [
        f"{inf}vIET = ( {inf} - INFTEFF_NSA ) / INFTEBASIS",
    ]

    dfa = msp.panel_calculator(dfx, calcs=calcs, cids=cids) # This scaling of the excess inflation is a standard procedure to make the effects of inflation changes comparable across the range of 
    # of high and low inflation countries.
    
    dfx = msm.update_df(dfx, dfa)

# The next step is calculation of the simple average of the three excess inflation metrics: 

calcs = [] 
for cp in ["CPIH", "CPIC"]:
    for v in ["vIET"]:
        calc = f"{cp}_SA_PALL{v} = ( {cp}_SA_P1M1ML12{v} + {cp}_SJA_P6M6ML6AR{v} + {cp}_SJA_P3M3ML3AR{v} ) / 3"
        calcs += [calc]

dfa = msp.panel_calculator(dfx, calcs, cids=cids)
dfx = msm.update_df(dfx, dfa)

# Lastly we calculate simple averages of USD-EUR inflation metrics: 

calcs = [
    "iUSD_iEUR_CPIH_SA_PALLvIET = ( iUSD_CPIH_SA_PALLvIET +  iEUR_CPIH_SA_PALLvIET ) / 2",   # USD-EUR inflation
    "iUSD_iEUR_CPIH_SJA_P6M6ML6ARvIET = ( iUSD_CPIH_SJA_P6M6ML6ARvIET +  iEUR_CPIH_SJA_P6M6ML6ARvIET ) / 2",
    "iUSD_CPIC_SJA_P6M6ML6ARvIET = iUSD_CPIC_SJA_P6M6ML6ARvIET"]
    
dfa = msp.panel_calculator(dfx, calcs, cids=cids)
dfx = msm.update_df(dfx, dfa)

Inflation and government bond returns #

In the United States, core PCE inflation is the key price indicator for monetary policy. In the presence of some rational inattention to price trends and their implication for Federal Reserve words and actions, we would expect core inflation above target to predict subsequent Treasure bond returns negatively. Indeed the relation between excess core inflation and subsequent 5-year IRS bomd returns has been negative and significantly so, at a weekly, monthly, and quarterly frequency. 

cr_bond = msp.CategoryRelations(
    dfx,
    xcats=["CPIC_SJA_P6M6ML6ARvIET", "GB05YR_NSA"],
    cids=["USD"],
    freq="M",
    lag=1,
    xcat_aggs=["last", "sum"],
    start="1990-01-01",
)

cr_bond.reg_scatter(
    title="Excess core inflation and subsequent 5-year government bond return for the US, since 2000",
    labels=False,
    coef_box="upper left",
    xlab="Core CPI inflation rate, %ar, versus effective inflation target, end-of-month information state",
    ylab="Next month's return on 5-year government bond return, %",
    prob_est="map"
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/51b5a216768e3c8586d6d01fb7fa1db3ffbfb88d80fbd487d09a6401cee1c9c7.png

Inflation as a predictor of IRS returns #

Excess inflation, above effective targets, has also negatively predicted interest rate swap reciver returns, at various frequencies and tenors. Generally, predictive correlation has been stronger for shorter-maturity contracts. 

cr_du = msp.CategoryRelations(
    dfx,
    xcats=["CPIH_SA_PALLvIET", "DU02YXR_VT10"],
    cids=cids_dmca, 
    freq="Q",
    lag=1,
    xcat_aggs=["last", "sum"],
    start="2000-01-01",
)

cr_du.reg_scatter(
    title="Inflation and subsequent IRS fixed receiver returns in developed markets, since 2000",
    labels=False,
    coef_box="lower left",
    xlab="Headline excess CPI inflation rate (average of various metrics), %ar, versus effective inflation target, end-of-month",
    ylab="Next quarter's return on 2-year IRS return, vol-targeted position, %",
    prob_est="map"
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/5be5b7ba81c7117b80cc85057a98e70a6a0514628ad7740144005248587e9c81.png

The negative predictive correlation between inflation and fixed receiver contract returns has been even stronger if one uses average U.S. and euro-area excess inflation as predictors for all developed countries, testifying to the dominance of these two economic areas and central banks for global interest rate markets. However, statistical significance has been a bit lower because the choice of communal predictors means less cross-country variation and an inability to draw lessons from cross-country inflation differences. 

cr_du = msp.CategoryRelations(
    dfx,
    xcats=["iUSD_iEUR_CPIH_SJA_P6M6ML6ARvIET", "DU02YXR_VT10"],
    cids=cids_dmca,
    freq="Q",
    lag=1,
    xcat_aggs=["last", "sum"],
    start="2000-01-01",
)

cr_du.reg_scatter(
    title="Average US-Euro adjusted headline consumer price trend and subsequent IRS returns in developed markets, since 2000",
    labels=False,
    coef_box="lower left",
    xlab="Average US-Euro adjusted headline consumer price trend: % 6m/6m ar, versus effective inflation target, end-of-month information state",
    ylab="Next quarter's return on 2-year IRS return, vol-targeted position, %",
    prob_est="map"
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/9049fa0cef28ccd970bcbefe46a8910a5809a06965ace7c79df2f40e634287e9.png

The predictive correlation of excess inflation in the G2 and subsequent monthly IRS receiver returns has been negative across all developed markets. This has not been the case for predictive correlations between local inflation: In Switzerland and Japan, the relation between inflation and subsequent receiver returns has been slightly positive. Presumably, in deflationary economies with zero or sub-zero policy rates inflation trends did little to affect short-term rates expectations over the past decades. 

srr_du = mss.SignalReturnRelations(
    dfx,
    cids=cids_dmca,
    sigs= "iUSD_iEUR_CPIH_SJA_P6M6ML6ARvIET",
    sig_neg=[True],
    rets=["DU02YXR_VT10"],
    freqs=["M"],
    start="2000-01-01",
)

srr_du.correlation_bars(
    title = "Correlation of excess headline inflation (%6m/6m, saar) in the G2 and subsequent 2-year IRS returns", 
    size=(12, 6)
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/9d5c0f6a0cd1955733ddba001a06065782ab3a1ea1c38b73991c16dd6222fc58.png

U.S. and euro area excess inflation also predicted emerging markets’ rate performances negatively. The predictive power has been stronger for the U.S. alone since the U.S. dollar is the dominant EM funding currency. Typically, high inflation in the G2 supports policy tightening in the large financial markets, which subsequently puts pressure on global capital flows and emerging market currencies, which then necessitates higher local rates in EM countries. 

# we take out bad-data return periods for fixed income markets
filt_try = (dfx["cid"] == "TRY") & (dfx["real_date"] > pd.to_datetime("2022-08-01"))
dfx.loc[filt_try, "value"] = np.nan

cr_du = msp.CategoryRelations(
    dfx,
    xcats=["iUSD_CPIC_SJA_P6M6ML6ARvIET", "DU02YXR_VT10"],
    cids = cids_em,
    freq="M",
    lag=1,
    xcat_aggs=["last", "sum"],
    xcat_trims=[20,20],
    start="2000-01-01",
)

cr_du.reg_scatter(
    title="Inflation and subsequent IRS returns in all available emerging markets countries, since 2000",
    labels=False,
    coef_box="lower left",
    xlab="USD headline CPI inflation rate, %ar, versus effective inflation target, end-of-month information state",
    ylab="Next month's return on 2-year IRS return, vol-targeted position, %",
    prob_est="map", 
      
)

DU02YXR_VT10 misses: ['BRL', 'PEN', 'PHP', 'RON'].
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/f7dcbbe97589276116a34662ebbdaac163959d49f781cde589187c599255b5b3.png

The negative predictive relation between U.S. excess inflation and EM fixed IRS receivers has been significant individually in most markets. Also, the predictive relation was negative across currency areas, with China being the only exception. 

srr_du = mss.SignalReturnRelations(
    dfx,
    cids=cids_em,
    sigs="iUSD_CPIC_SJA_P6M6ML6ARvIET",
    sig_neg=True,
    rets="DU02YXR_VT10",
    freqs=["M"],
    start="2000-01-01",
)

srr_du.correlation_bars(
    title="Correlation probability of excess USD inflation with subsequent 2 years IRS returns in EM since 2000",
    size=(12, 6),
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/b045b8d0533da5303f0d8654e99b0171d925f0f52316d63211368fc6b371ad56.png

Inflation as a predictor of relative IRS returns #

Here, we define relative headline or core inflation as the average (%oya, %6m/6m, saar, %3m/3m, saar) excess inflation rate of one (developed market) currency area versus the average of all currency areas. 

dfa = msp.make_relative_value(
    dfx,
    xcats=["DU02YXR_VT10", "DU05YXR_VT10", "CPIH_SA_PALLvIET", "CPIC_SA_PALLvIET"],
    cids=cids_dmca,
    postfix="vDM",
)
dfx = msm.update_df(dfx, dfa)

xcatx = ["CPIH_SA_PALLvIETvDM", "CPIC_SA_PALLvIETvDM"]


msp.view_timelines(
    dfx,
    xcats=xcatx,
    cids=cids_dmca,
    ncol=3,
    cumsum=False,
    start="2000-01-01",
    same_y=False,
    all_xticks=True,
    title="Relative excess inflation trends versus DM basket",
    xcat_labels=None,
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/e8e87e0522400b530c86982111ae4f0537d0d93c06c820e63844e2163633d980.png

Relative excess inflation, whether headline or core, has also been negatively and significantly correlated with subsequent IRS returns, across 2-year and 5-year tenors and for weekly, monthly, and quarterly frequencies. 

crx = msp.CategoryRelations(
    dfx,
    xcats=["CPIH_SA_PALLvIETvDM", "DU05YXR_VT10vDM"],
    cids=cids_dmca,
    freq="Q",
    lag=1,
    xcat_aggs=["last", "sum"],
    start="2000-01-01",
    xcat_trims=[None, None],
)
crx.reg_scatter(
    labels=False,
    coef_box="lower left",
    xlab="Headline CPI, % 6m/6m ar, seasonally adjusted, point-in-time, versus DM basket",
    ylab="5-year IRS receiver return, 10% vol target, versus a basket of 10 countries",
    title="Relative headline CPI trend and subsequent relative 5-year IRS receiver returns",
    size=(12, 8),
    prob_est="map",
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/a472c421c30f1382e7462187864022ae31dfca8a907458c1feb0785c2323dad0.png

Inflation as a predictor of equity returns #

Excess inflation and changes in inflation have been negatively correlated with subsequent equity index future returns since 2000 for developed countries. However, the relations have not (yet) been statistically significant, according to the Macrosynergy panel test. The apparent negative correlation of the pooled dataset in a scatterplot is actually misleading. This is because most of the negative relation comes from 1 or 2 episodes of accelerating and slowing CPIs around the great financial crisis and the COVID-19 pandemic, which are (pseudo-) replicated across all markets. The relation has been consistent, and relative inflation differentials have not strongly predicted relative equity returns. 

cr_eq = msp.CategoryRelations(
    dfx,
    xcats=["CPIH_SA_PALLvIET", "EQXR_VT10"],
    cids = cids_dmca,
    freq="M",
    lag=1,
    xcat_aggs=["last", "sum"],
    start="2000-01-01",
)

cr_eq.reg_scatter(
    title="Excess headline CPI inflation and subsequent equity market returns (since 2000)",
    labels=False,
    coef_box="lower left",
    xlab="Headline inflation versus effective inflation target, end-of-month information state",
    ylab="Next quarter's equity return, vol-targeted position, %",
    prob_est="map"
)

EQXR_VT10 misses: ['NOK', 'NZD'].
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/61dbff983d0a77e46e7a5ab174cb8798862bb548b23e70f6053570ea894a2e85.png 
cr_eq = msp.CategoryRelations(
    dfx,
    xcats=["CPIH_SA_P1M1ML12_D1M1ML3", "EQXR_VT10"],
    cids = cids_dmca,
    freq="M",
    lag=1,
    xcat_aggs=["last", "sum"],
    start="2000-01-01",
)

cr_eq.reg_scatter(
    title="Information states of headline inflation changes and subsequent index futures returns (since 2000)",
    labels=False,
    coef_box="lower left",
    xlab="Change in headline inflation (%oya) over the latest 3 reported months, information state at month end",
    ylab="Next month's equity return, vol-targeted position, %",
    prob_est="map"
)

EQXR_VT10 misses: ['NOK', 'NZD'].
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/67468aa0e0cdb6edca493fb86e3074701962531129e2bdb700a4c4b1d2f7edb8.png

Excess average USD euro zone inflation is negatively correlated with subsequent equity index future returns since 2000 using all available countries. This relation has been statistically significant, according to the Macrosynergy panel test, and consistent. This suggests that inflation has been an important predictor of equity returns in the large markets and - hence - globally. However, inflation differentials across countries have not been a powerful predictor. 

cids_EQXR_NSA = dfx[dfx["xcat"] == "EQXR_NSA"]["cid"].unique()
cids_iUSD_iEUR_CPIH_SJA_P6M6ML6ARvIET = dfx[dfx["xcat"] == "iUSD_iEUR_CPIH_SJA_P6M6ML6ARvIET"]["cid"].unique()
common_cids = np.intersect1d(cids_EQXR_NSA, cids_iUSD_iEUR_CPIH_SJA_P6M6ML6ARvIET)

cr_eq = msp.CategoryRelations(
    dfx,
    xcats=["iUSD_iEUR_CPIH_SJA_P6M6ML6ARvIET", "EQXR_NSA"],
    cids = common_cids,
    freq="M",
    lag=1,
    xcat_aggs=["last", "sum"],
    start="2000-01-01",
)

cr_eq.reg_scatter(
    title="Excess headline inflation (%6m/6m, saar) in the G2 and subsequent equity market returns (since 2000)",
    labels=False,
    coef_box="lower left",
    xlab="Headline inflation versus effective inflation target, end-of-month information state",
    ylab="Next month's equity return, %",
    prob_est="map"
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/ec15e3d472b60408afce7e59e951e65c7914a391e44b08a09a8e709d51b071fc.png 
srr_eq = mss.SignalReturnRelations(
    dfx,
    cids=list(dfx[dfx["xcat"] == "EQXR_NSA"]["cid"].unique()),
    sigs= "iUSD_iEUR_CPIH_SJA_P6M6ML6ARvIET", 
    sig_neg=[True],
    rets=["EQXR_NSA"],
    freqs=["M"],
    start="2000-01-01",
)


srr_eq.correlation_bars(
    title="Correlation probability of excess average USD euro zone inflation with subsequent equity returns since 2000",
    size=(12, 6),
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/7a75844a12a0169dc29f9a9c8c56fe8899f4038266a561862476a5340b381320.png

Inflation as a predictor of directional FX returns #

The main hypothesis for the relation between inflation and FX forward returns is that higher excess inflation triggers tighter monetary policy and a strong currency. For this to hold logically, we must look at excess inflation differentials of various currencies against their natural benchmarks, against the most frequently quoted base currency. This is the dollar for most, but the euro for CHF, CZK, HUF, NOK, PLN, RON, SEK. and both dollar and euro for GBP, RUB, TRY.

The computed excess inflation ratios will be designated with the suffix _vBM 

cids_fx = list(set(cids) - set(["EUR", "USD"]))
cids_eur = ["CHF", "CZK", "HUF", "NOK", "PLN", "RON", "SEK"]  # trading against EUR
cids_eud = ["GBP", "RUB", "TRY"]  # trading against EUR and USD
cids_usd = list(set(cids_fx) - set(cids_eur + cids_eud))  # trading against USD


xcatx = ["CPIH_SJA_P6M6ML6ARvIET", "CPIC_SJA_P6M6ML6ARvIET", "CPIC_SA_P1M1ML12_D1M1ML3", "CPIC_SJA_P3M3ML3AR", "CPIH_SJA_P3M3ML3AR"]

for xc in xcatx:
    calc_eur = [f"{xc}vBM = {xc} - iEUR_{xc}"]
    calc_usd = [f"{xc}vBM = {xc} - iUSD_{xc}"]
    calc_eud = [f"{xc}vBM = {xc} - 0.5 * ( iEUR_{xc} + iUSD_{xc} )"]

    dfa_eur = msp.panel_calculator(
        dfx,
        calcs=calc_eur,
        cids=cids_eur,
    )
    dfa_usd = msp.panel_calculator(
        dfx,
        calcs=calc_usd,
        cids=cids_usd,
    )
    dfa_eud = msp.panel_calculator(
        dfx,
        calcs=calc_eud,
        cids=cids_eud,
    )

    dfa = pd.concat([dfa_eur, dfa_usd, dfa_eud])
    dfx = msm.update_df(dfx, dfa)

Indeed, the relationship between relative excess inflation rates and subsequent FX forward returns has been strongly and significantly positive for developed market currencies at various frequencies. 

cids_dmfx =(list(set(cids_dmca) - set(["USD", "EUR"]))) # DM currencies excluding USD, EUR

crx = msp.CategoryRelations(
    dfx,
    xcats=["CPIH_SJA_P6M6ML6ARvIETvBM", "FXXR_VT10"],
    cids=cids_dmfx,
    freq="Q",
    lag=1,
    xcat_aggs=["last", "sum"],
    xcat_trims=[20,20 ], 
    start="2000-01-01",
   
  
)
crx.reg_scatter(
    labels=False,
    coef_box="lower left",
    xlab="Headline CPI, % 6m/6m saar, versus base currency",
    ylab="1-month FX forward return, 10% vol target, local versus base currency",
    title="Excess relative headline inflation and next quarter's FX return, developed markets since 2000",
    prob_est="map",
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/13bfbd4176396940a29dee9af5eec1f0efba4c71ad220253672cb9aca1e26e5f.png

The positive relationship between excess inflation differentials and subsequent FX returns has been similarly strong and significant for emerging markets. 

crx = msp.CategoryRelations(
    dfx,
    xcats=["CPIH_SJA_P6M6ML6ARvIETvBM", "FXXR_VT10"],
    cids=cids_em,
    freq="Q",
    lag=1,
    xcat_aggs=["last", "sum"],
    xcat_trims=[20,20 ], 
    start="2000-01-01",
   
  
)
crx.reg_scatter(
    labels=False,
    coef_box="lower left",
    xlab="Headline CPI, % 6m/6m saar, versus base currency",
    ylab="1-month FX forward return, 10% vol target, local versus base currency",
    title="Excess relative headline inflation and next quarter's FX return, emerging markets since 2000",
    prob_est="map",
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/6d2586514007fb925a862f5fc378fba233b8463dd2368736367d557f46c09ac4.png

Inflation as a predictor of relative FX returns #

There has also been a strong “double relative” relation between excess inflation, against base currency and a basket of currencies, and FX forward returns, again against base and against a basket of developed market currencies. This predictive relation is valuable because it allows creating a more diversified FX portfolio and reduces the dominant influence of dollar and euro against all other currencies. 

dfa = msp.make_relative_value(
    dfx, xcats=["CPIH_SJA_P6M6ML6ARvIETvBM", "FXXR_VT10"], cids=cids_dmfx, postfix="vDM"
)
dfx = msm.update_df(dfx, dfa)


crx_fxrel = msp.CategoryRelations(
    dfx,
    xcats=["CPIH_SJA_P6M6ML6ARvIETvBMvDM", "FXXR_VT10vDM"],
    cids=cids_dmfx,
    freq="Q",
    lag=1,
    xcat_aggs=["last", "sum"],
    start="2000-01-01",
    xcat_trims=[10, 30],
)
crx_fxrel.reg_scatter(
    labels=False,
    coef_box="lower left",
    xlab="Headline CPI, % 6m/6m ar, seasonally and jump adjusted, versus base currency and DM basket",
    ylab="1-month FX forward return, 10% vol target, versus base currency and DM basket",
    title="Excess core inflation trend versus basket and next quarter's FX forward return (DM)",
    prob_est="map",
)
https://macrosynergy.com/notebooks.build/themes/economic-trends/_images/8b1f600519d9c2e8a25b1e888f579e89740871538956d1ad481fe0a6d32e2d16.png

Appendices #

Appendix 1: Volatile component exclusions from core CPI calculations #

Core CPI refers to a CPI that excludes volatile price components according to preferred local convention. The excluded items are as follows:

  • AUD: fruit, vegetables and automotive fuel.

  • BRL: fuel for domestic and for automobile use and 10 items of the food and beverages group.

  • CAD: eight of the most volatile components identified by the Bank of Canada, which are fruit, fruit preparations and nuts, vegetables and vegetable preparations, mortgage interest cost, natural gas, fuel oil and other fuels, gasoline, inter-city transportation, and tobacco products and smokers’ supplies.

  • CHF: food, beverages, tobacco, seasonal products, energy and fuel.

  • CLP: food and energy/ fruit, fresh vegetables and fuel.

  • CNY: food and energy.

  • COP: basic expenses which recorded the largest price volatility and represents 20% of the CPI basket.

  • CZK: effects of tax adjustments and changes in regulated prices and other administrative measures.

  • EUR: food and energy.

  • GBP: energy, food, alcohol and tobacco.

  • HUF: non-processed food items, electricity gas and other fuels, motor fuels and oils, pharmaceutical products that are reimbursed by the social security, services prices thatare centrally determined by authorities.

  • IDR: volatile foods and administered prices, such as subsidized fuel, electricity rates and transportation fares.

  • ILS: housing, fruits and vegetables.

  • INR: food & non-alcholic beverages (JPMaQS calculation).

  • JPY: food (ex alcoholic beverages) and energy/ fresh food.

  • KRW: food & energy.

  • MXN: all that is not in the ‘subyacente’ component is composed by goods and services for which the variation in prices is caused by market conditions.

  • MYR: food.

  • NOK: tax effects and energy products/ electricity.

  • NZD: food, household energy and vehicle fuels.

  • PEN: food and energy.

  • PHP: food.

  • PLN: food and energy.

  • RON: vegetables, fruit, eggs, fuels and administered prices/ administered prices and highly volatile prices (vegetables, fruit, eggs, fuels).

  • RUB: fruits and vegetables, fuel and administrative prices.

  • SEK: energy.

  • SGD: accommodation and private transport.

  • THB: raw food and energy.

  • TRY: energy, food, all beverages, tobacco products and gold.

  • TWD: fruits, vegetables and energy.

  • USD: food and energy.

  • ZAR: food, non-alcoholic beverages, petrol and energy.

For the explanation of currency symbols, which are related to currency areas or countries for which categories are available, please view the subsequent appendix.

Appendix 2: Early CPI estimates #

JPMaQS employs two methods for estimating monthly CPI values prior to the official release for a month.

The first is used when the early indicator is a broad CPI-like index. In this case the estimated CPI is simply the monthly change ratio of the early indicator (EI) times the latest available official CPI.

\[ Est(CPI_{t}) = CPI_{t-1} * \frac{EI_t}{EI_{t-1}}. \]

The second method is applied when the early indicator is a narrower subset of the CPI or a single price. In this case we first run rolling regressions of changes in annual rates in early CPI on concurrent changes in the early indicator. In a case of negative coefficent we set \(\beta_t\) equal to zero.

\[ \frac{CPI_t}{CPI_{t-12}}-\frac{CPI_{t-1}}{CPI_{t-13}} = \beta_t * (\frac{EI_t}{EI_{t-12}}-\frac{EI_{t-1}}{EI_{t-13}}) \]

Then we use the estimated coefficient based on past history and the change in annual growth rates of the early indicator to predict the latest month’s CPI:

\[ Est(CPI_{t}) = CPI_{{t-12}}*(\frac{CPI_{t-1}}{CPI_{t-13}}+Est(\beta_t) * (\frac{EI_t}{EI_{t-12}}-\frac{EI_{t-1}}{EI_{t-13}})) \]

Appendix 3: Currency symbols #

The word ‘cross-section’ refers to currencies, currency areas or economic areas. In alphabetical order, these are AUD (Australian dollar), BRL (Brazilian real), CAD (Canadian dollar), CHF (Swiss franc), CLP (Chilean peso), CNY (Chinese yuan renminbi), COP (Colombian peso), CZK (Czech Republic koruna), DEM (German mark), ESP (Spanish peseta), EUR (Euro), FRF (French franc), GBP (British pound), HKD (Hong Kong dollar), HUF (Hungarian forint), IDR (Indonesian rupiah), ITL (Italian lira), JPY (Japanese yen), KRW (Korean won), MXN (Mexican peso), MYR (Malaysian ringgit), NLG (Dutch guilder), NOK (Norwegian krone), NZD (New Zealand dollar), PEN (Peruvian sol), PHP (Phillipine peso), PLN (Polish zloty), RON (Romanian leu), RUB (Russian ruble), SEK (Swedish krona), SGD (Singaporean dollar), THB (Thai baht), TRY (Turkish lira), TWD (Taiwanese dollar), USD (U.S. dollar), ZAR (South African rand).

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By Macrosynergy Ltd.

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