P1 · Instructor build — the weekly tracker

Four public series, one factor, GDP units

Author

Tyler Sotomayor

Published

July 30, 2026

This is the worked benchmark for Practicum 1: a weekly economic activity tracker in the spirit of Lewis et al. (2022), built from four public FRED series, scaled to GDP units, and judged against the official Weekly Economic Index. Everything below executes top to bottom; re-rendering this page re-pulls the data.

Vintage honesty, up front

This build uses today’s FRED data, which is revised. Initial claims in particular are revised every week for several weeks after first release. A production version must pull ALFRED vintages so the tracker on date t uses only what was known on date t — that is the stretch goal in the brief, and nothing in this page’s backtest should be quoted as “real-time performance.”

Pull

Four weekly inputs (two labor, two credit), two official benchmarks, one quarterly target — all from FRED’s keyless CSV endpoint.

Code

import io, urllib.request
import numpy as np
import pandas as pd

def fred(series_id: str) -> pd.Series:
    """One series from FRED's public CSV endpoint, date-indexed."""
    url = f"https://fred.stlouisfed.org/graph/fredgraph.csv?id={series_id}"
    with urllib.request.urlopen(url) as r:
        df = pd.read_csv(io.BytesIO(r.read()), na_values=".",
                         parse_dates=["observation_date"])
    return df.set_index("observation_date")[series_id].astype(float)

INPUTS = {
    "ICSA":           ("initial claims", -1),        # countercyclical
    "CCSA":           ("continued claims", -1),      # countercyclical
    "TOTBKCR":        ("bank credit", +1),
    "CCLACBW027SBOG": ("consumer loans", +1),
}
raw  = {sid: fred(sid) for sid in INPUTS}
wei  = fred("WEI")      # official Weekly Economic Index (Lewis et al.)
gdp  = fred("GDPC1")    # real GDP, quarterly

latest = max(s.index.max() for s in raw.values())
print(f"Latest weekly observation: {latest:%Y-%m-%d}")

Latest weekly observation: 2026-07-18

Transform

Following Lewis et al., each input becomes a 52-week log difference — a year-over-year growth rate that needs no seasonal adjustment, because it compares each week to the same week a year earlier. Claims enter negated (rising claims = falling activity). Everything is aligned to Saturday-ended weeks and standardized over the common sample.

Code

def yoy(s: pd.Series) -> pd.Series:
    w = s.resample("W-SAT").last()
    return 100 * np.log(w / w.shift(52))

panel = pd.DataFrame({
    name: sign * yoy(raw[sid])
    for sid, (name, sign) in INPUTS.items()
}).dropna()
print(f"Common sample: {panel.index.min():%Y-%m-%d} → {panel.index.max():%Y-%m-%d}"
      f"  ({len(panel)} weeks × {panel.shape[1]} series)")

Common sample: 2001-06-30 → 2026-07-11  (1307 weeks × 4 series)

The standardization trap (found the hard way)

The obvious next step — standardize each series over the full sample — is wrong, and the first draft of this build made exactly that mistake. In April 2020 initial claims ran near eight standard deviations from normal; a full-sample standard deviation is so inflated by those weeks that the Great Recession shrinks to about -1.4\sigma and the fitted tracker barely registers 2009 at all. The build journal shows the broken figure. The fix: calibrate on the pre-2020 sample — means, variances, factor weights, and the GDP scaling — then apply those fixed weights to the whole history, so extreme episodes are measured on a normal-times yardstick rather than allowed to redefine it.

Code

CAL = panel.loc[:"2019-12-31"]                 # calibration window
z   = (panel - CAL.mean()) / CAL.std()         # normal-times yardstick

Extract

The first principal component — weights estimated on the calibration window, then applied to the full history. This is the “one number” summary of the panel, and the static cousin of the dynamic factor model we build in Session 2.

Code

zc = z.loc[:"2019-12-31"]
U, S, Vt = np.linalg.svd(zc.values, full_matrices=False)
w = Vt[0]
factor = pd.Series(z.values @ w, index=z.index, name="factor")
if factor.corr(z["initial claims"]) < 0:      # sign convention: pro-cyclical
    factor, w = -factor, -w

share = S[0]**2 / (S**2).sum()
print(f"First PC explains {share:.0%} of pre-2020 panel variance")
print(pd.Series(w, index=z.columns).round(2).to_string())

First PC explains 48% of pre-2020 panel variance
initial claims      0.69
continued claims    0.69
bank credit        -0.08
consumer loans      0.20

Scale

A factor has no units. Regress four-quarter GDP growth on the quarterly average of the factor — again on the calibration window only — and the fitted line converts the weekly factor into “GDP growth over the past year, in percent”, the same units the WEI reports.

Code

gdp_yoy  = (100 * np.log(gdp / gdp.shift(4))).dropna()
f_q      = factor.resample("QS").mean()
both     = pd.concat([f_q, gdp_yoy], axis=1, keys=["f", "g"]).dropna()
cal      = both.loc[:"2019-12-31"]

b, a = np.polyfit(cal["f"], cal["g"], 1)
tracker  = a + b * factor
resid    = cal["g"] - (a + b * cal["f"])
r2       = 1 - resid.var() / cal["g"].var()
print(f"tracker = {a:.2f} + {b:.2f} × factor   (pre-2020 quarterly R² = {r2:.2f})")

tracker = 2.05 + 0.90 × factor   (pre-2020 quarterly R² = 0.63)

Judge

Code

import matplotlib.pyplot as plt

INK, MUT, BLUE, ORANGE = "#52514e", "#898781", "#2a78d6", "#eb6834"
def style(ax):
    for side in ("top", "right"): ax.spines[side].set_visible(False)
    for side in ("left", "bottom"): ax.spines[side].set_color(MUT)
    ax.tick_params(colors=MUT, labelsize=9)
    ax.figure.patch.set_alpha(0); ax.patch.set_alpha(0)

common = pd.concat([tracker, wei], axis=1, keys=["ours", "wei"]).dropna()
corr = common["ours"].corr(common["wei"])

fig, ax = plt.subplots(figsize=(9.5, 4.2), dpi=150)
sub = common.loc["2008":]
ax.axhline(0, color="#c3c2b7", lw=1)
ax.plot(sub.index, sub["wei"],  color=ORANGE, lw=1.4, label="official WEI (10 series)")
ax.plot(sub.index, sub["ours"], color=BLUE,   lw=1.6, label="this tracker (4 series)")
ax.set_ylabel("GDP growth, trailing year (%)", color=INK, fontsize=9)
ax.legend(frameon=False, fontsize=9, labelcolor=INK)
ax.set_title(f"correlation {corr:.2f} on the common sample", loc="left",
             fontsize=9, color=MUT)
style(ax); plt.tight_layout(); plt.show()

Figure 1: The four-series tracker against the official ten-series WEI. One factor, public data only.

Code

fig, ax = plt.subplots(figsize=(9.5, 3.6), dpi=150)
sub = common.loc["2019-07":"2021-12"]
ax.axhline(0, color="#c3c2b7", lw=1)
ax.plot(sub.index, sub["wei"],  color=ORANGE, lw=1.4, label="official WEI")
ax.plot(sub.index, sub["ours"], color=BLUE,   lw=1.6, label="this tracker")
g = gdp_yoy.loc["2019-07":"2021-12"]
ax.scatter(g.index + pd.Timedelta(days=45), g, color=INK, s=18, zorder=5,
           label="GDP growth (quarterly, plotted mid-quarter)")
ax.legend(frameon=False, fontsize=9, labelcolor=INK)
style(ax); plt.tight_layout(); plt.show()

Figure 2: The reason weekly trackers exist: the 2020 collapse and rebound, visible months before quarterly GDP.

What the comparison teaches

Correlation with official WEI: 0.90
Largest divergence: 2020-03-28 (-11.4pp)

Four public series recover most of what ten curated ones deliver — that is the factor-model promise in miniature: the business cycle is low-dimensional, so a handful of noisy witnesses, properly weighted, testify to it well. The divergences are as instructive as the agreement: our credit-heavy panel misses sectors (retail, energy, staffing) the official WEI sees, and its largest gaps cluster where those sectors moved independently of labor and credit. More and better series is one fix; the Session 2 dynamic factor model — which handles ragged edges and lets the factor have dynamics — is the other, and it is where this course goes next.

References

Lewis, Daniel J., Karel Mertens, James H. Stock, and Mihir Trivedi. 2022. “Measuring Real Activity Using a Weekly Economic Index.” Journal of Applied Econometrics 37 (4): 667–87.

--- title: "P1 · Instructor build — the weekly tracker" subtitle: "Four public series, one factor, GDP units" author: "Tyler Sotomayor" date: 2026-07-30 css: [../../../sessions/notes-ebook.css] bibliography: ../../../sessions/01-state-space-kalman/references.bib execute: freeze: true warning: false format: html: include-after-body: ../../../sessions/notes-font-toggle.html code-fold: show code-tools: true --- This is the worked benchmark for [Practicum 1](../index.qmd): a weekly economic activity tracker in the spirit of @lewis2022weekly, built from **four public FRED series**, scaled to GDP units, and judged against the official Weekly Economic Index. Everything below executes top to bottom; re-rendering this page re-pulls the data. ::: {.callout-warning} ## Vintage honesty, up front This build uses **today's FRED data**, which is revised. Initial claims in particular are revised every week for several weeks after first release. A production version must pull ALFRED vintages so the tracker on date $t$ uses only what was known on date $t$ — that is the stretch goal in the brief, and nothing in this page's backtest should be quoted as "real-time performance." ::: ## Pull Four weekly inputs (two labor, two credit), two official benchmarks, one quarterly target — all from FRED's keyless CSV endpoint. ```{python} import io, urllib.request import numpy as np import pandas as pd def fred(series_id: str) -> pd.Series: """One series from FRED's public CSV endpoint, date-indexed.""" url = f"https://fred.stlouisfed.org/graph/fredgraph.csv?id={series_id}" with urllib.request.urlopen(url) as r: df = pd.read_csv(io.BytesIO(r.read()), na_values=".", parse_dates=["observation_date"]) return df.set_index("observation_date")[series_id].astype(float) INPUTS = { "ICSA": ("initial claims", -1), # countercyclical "CCSA": ("continued claims", -1), # countercyclical "TOTBKCR": ("bank credit", +1), "CCLACBW027SBOG": ("consumer loans", +1), } raw = {sid: fred(sid) for sid in INPUTS} wei = fred("WEI") # official Weekly Economic Index (Lewis et al.) gdp = fred("GDPC1") # real GDP, quarterly latest = max(s.index.max() for s in raw.values()) print(f"Latest weekly observation: {latest:%Y-%m-%d}") ``` ## Transform Following Lewis et al., each input becomes a **52-week log difference** — a year-over-year growth rate that needs no seasonal adjustment, because it compares each week to the same week a year earlier. Claims enter negated (rising claims = falling activity). Everything is aligned to Saturday-ended weeks and standardized over the common sample. ```{python} def yoy(s: pd.Series) -> pd.Series: w = s.resample("W-SAT").last() return 100 * np.log(w / w.shift(52)) panel = pd.DataFrame({ name: sign * yoy(raw[sid]) for sid, (name, sign) in INPUTS.items() }).dropna() print(f"Common sample: {panel.index.min():%Y-%m-%d} → {panel.index.max():%Y-%m-%d}" f" ({len(panel)} weeks × {panel.shape[1]} series)") ``` ::: {.callout-important} ## The standardization trap (found the hard way) The obvious next step — standardize each series over the full sample — is **wrong**, and the first draft of this build made exactly that mistake. In April 2020 initial claims ran near eight standard deviations from normal; a full-sample standard deviation is so inflated by those weeks that the Great Recession shrinks to about $-1.4\sigma$ and the fitted tracker barely registers 2009 at all. The [build journal](../journal.qmd) shows the broken figure. The fix: **calibrate on the pre-2020 sample** — means, variances, factor weights, and the GDP scaling — then apply those fixed weights to the whole history, so extreme episodes are *measured* on a normal-times yardstick rather than allowed to redefine it. ::: ```{python} CAL = panel.loc[:"2019-12-31"] # calibration window z = (panel - CAL.mean()) / CAL.std() # normal-times yardstick ``` ## Extract The first principal component — weights estimated on the calibration window, then applied to the full history. This is the "one number" summary of the panel, and the static cousin of the dynamic factor model we build in Session 2. ```{python} zc = z.loc[:"2019-12-31"] U, S, Vt = np.linalg.svd(zc.values, full_matrices=False) w = Vt[0] factor = pd.Series(z.values @ w, index=z.index, name="factor") if factor.corr(z["initial claims"]) < 0: # sign convention: pro-cyclical factor, w = -factor, -w share = S[0]**2 / (S**2).sum() print(f"First PC explains {share:.0%} of pre-2020 panel variance") print(pd.Series(w, index=z.columns).round(2).to_string()) ``` ## Scale A factor has no units. Regress four-quarter GDP growth on the quarterly average of the factor — again on the calibration window only — and the fitted line converts the weekly factor into **"GDP growth over the past year, in percent"**, the same units the WEI reports. ```{python} gdp_yoy = (100 * np.log(gdp / gdp.shift(4))).dropna() f_q = factor.resample("QS").mean() both = pd.concat([f_q, gdp_yoy], axis=1, keys=["f", "g"]).dropna() cal = both.loc[:"2019-12-31"] b, a = np.polyfit(cal["f"], cal["g"], 1) tracker = a + b * factor resid = cal["g"] - (a + b * cal["f"]) r2 = 1 - resid.var() / cal["g"].var() print(f"tracker = {a:.2f} + {b:.2f} × factor (pre-2020 quarterly R² = {r2:.2f})") ``` ## Judge ```{python} #| label: fig-tracker #| fig-cap: "The four-series tracker against the official ten-series WEI. One factor, public data only." import matplotlib.pyplot as plt INK, MUT, BLUE, ORANGE = "#52514e", "#898781", "#2a78d6", "#eb6834" def style(ax): for side in ("top", "right"): ax.spines[side].set_visible(False) for side in ("left", "bottom"): ax.spines[side].set_color(MUT) ax.tick_params(colors=MUT, labelsize=9) ax.figure.patch.set_alpha(0); ax.patch.set_alpha(0) common = pd.concat([tracker, wei], axis=1, keys=["ours", "wei"]).dropna() corr = common["ours"].corr(common["wei"]) fig, ax = plt.subplots(figsize=(9.5, 4.2), dpi=150) sub = common.loc["2008":] ax.axhline(0, color="#c3c2b7", lw=1) ax.plot(sub.index, sub["wei"], color=ORANGE, lw=1.4, label="official WEI (10 series)") ax.plot(sub.index, sub["ours"], color=BLUE, lw=1.6, label="this tracker (4 series)") ax.set_ylabel("GDP growth, trailing year (%)", color=INK, fontsize=9) ax.legend(frameon=False, fontsize=9, labelcolor=INK) ax.set_title(f"correlation {corr:.2f} on the common sample", loc="left", fontsize=9, color=MUT) style(ax); plt.tight_layout(); plt.show() ``` ```{python} #| label: fig-covid #| fig-cap: "The reason weekly trackers exist: the 2020 collapse and rebound, visible months before quarterly GDP." fig, ax = plt.subplots(figsize=(9.5, 3.6), dpi=150) sub = common.loc["2019-07":"2021-12"] ax.axhline(0, color="#c3c2b7", lw=1) ax.plot(sub.index, sub["wei"], color=ORANGE, lw=1.4, label="official WEI") ax.plot(sub.index, sub["ours"], color=BLUE, lw=1.6, label="this tracker") g = gdp_yoy.loc["2019-07":"2021-12"] ax.scatter(g.index + pd.Timedelta(days=45), g, color=INK, s=18, zorder=5, label="GDP growth (quarterly, plotted mid-quarter)") ax.legend(frameon=False, fontsize=9, labelcolor=INK) style(ax); plt.tight_layout(); plt.show() ``` ## What the comparison teaches ```{python} #| echo: false gap = (common["ours"] - common["wei"]).loc["2008":] worst = gap.abs().idxmax() print(f"Correlation with official WEI: {corr:.2f}") print(f"Largest divergence: {worst:%Y-%m-%d} ({gap.loc[worst]:+.1f}pp)") ``` Four public series recover most of what ten curated ones deliver — that is the factor-model promise in miniature: the business cycle is *low-dimensional*, so a handful of noisy witnesses, properly weighted, testify to it well. The divergences are as instructive as the agreement: our credit-heavy panel misses sectors (retail, energy, staffing) the official WEI sees, and its largest gaps cluster where those sectors moved independently of labor and credit. More and better series is one fix; the Session 2 dynamic factor model — which handles ragged edges and lets the factor have dynamics — is the other, and it is where this course goes next.