U.S. Seasonally Adjusted All Items Consumer Price Index

USCPISA is the seasonally adjusted all-items consumer price index recorded as published, the monthly index-number level (1982–1984 = 100) that measures the average change over time in the prices consumers pay for a fixed basket of consumer goods and services. The seasonal adjustment belongs to the measurement basis by which the published level comes to exist, and KRED adds nothing to it. The same all-items basket is also compiled without seasonal adjustment and served separately as USCPI, so the two series are one measured price level on two conventions, the adjusted convention here and the as-observed convention there, and neither is a revision or a duplicate of the other.

This level is computed as a base-period-quantity-weighted aggregate, and because the weights are held fixed across the entire comparison, movements in the index reflect price change alone rather than shifts in basket composition (Laspeyres 1871).

The current-period-weighted counterpart and the ideal index that is the geometric mean of the two bound the fixed-base level from above and below, and this ideal index satisfies the time- and factor-reversal tests (Paasche 1874; Fisher 1922). The expenditure-share-weighted log-change form gives the superlative approximation against which the fixed-basket level is read (Törnqvist 1936).

The quantity the index ultimately approximates is the true cost-of-living index, the expenditure ratio that holds household utility fixed (Konüs 1939). That target is made precise within the four-approach taxonomy of index-number theory (Diewert 2002), whose economic approach is grounded in the exact and superlative aggregators (Diewert 1976).

Because the basket is held fixed, the level departs from the cost-of-living target by the substitution and quality-change wedge and by measurement bias (Diewert 1998; Boskin et al. 1996), while the axiomatic consistency the construction does satisfy belongs to the test-approach lineage (Balk 1995).

Seasonal adjustment removes the pattern that repeats within the year and leaves the price distribution itself untouched, so the level served here preserves the full distribution rather than the supply-shock-robust central tendency of core inflation (Eckstein 1981), and separating the persistent component from the transitory one remains a task for the reader (Cecchetti 1997).

KRED applies no transformation to USCPISA, loading the published index level as recorded with only a date parse and a reshape into the long store. It therefore performs no re-indexing, deflation, smoothing, annualizing, or year-over-year differencing, and it applies no seasonal filter of its own, since the adjustment already belongs to the measurement basis by which the published level comes to exist.

That measurement basis is fixed-basket aggregation, where a base-period expenditure survey fixes the quantity weights and the elementary price relatives are combined into the all-items index anchored at 1982–1984 = 100 (Laspeyres 1871).

The construction sits within the index-number framework whose alternatives are the current-weighted index, the symmetric ideal index, and the expenditure-share log-change index (Paasche 1874; Fisher 1922; Törnqvist 1936). The last two are the superlative formulas that are exact for flexible aggregators (Diewert 1976).

The four conceptual routes to the same number are the fixed-basket, test, stochastic, and economic approaches (Diewert 2002). The axiomatic properties this level satisfies are characterized within the test approach (Balk 1995), and the cost-of-living concept it targets is defined as the expenditure ratio that holds utility fixed (Konüs 1939).

The gap between the fixed-base level and that economic target consists of substitution bias and broader measurement bias, and because the series is served exactly as measured, KRED does not correct it (Diewert 1998; Boskin et al. 1996).

Removing the within-year pattern leaves the transitory disturbances in place, so the decomposition into trend, transitory disturbance, and bias is left to the user (Cecchetti 1997). Reaching an underlying-inflation reading from the same recorded basket would require either deleting the volatile strata before aggregation (Eckstein 1981) or summarizing the cross-section of component price changes with the limited-influence estimators and the kurtosis-optimal trimmed mean (Bryan and Cecchetti 1994; Bryan, Cecchetti, and Wiggins 1997). None of these constructions are applied to USCPISA itself, which remains at the recorded level.

As a measure of consumer prices, the index is the empirical counterpart of the cost-of-living concept, and its use as the operational target of price stability turns on how closely a fixed-basket level tracks that concept (Konüs 1939).

The headline reading economic agents respond to is a known upward-biased proxy for welfare-relevant inflation. The fixed-base level overstates true cost-of-living growth by a substitution wedge, and the combined commodity-substitution, outlet, quality-change, and new-goods bias widens that wedge (Laspeyres 1871; Diewert 1998; Boskin et al. 1996).

For monetary-policy purposes the headline level is routinely decomposed into a persistent component and transitory noise. This separation is framed as trend plus transitory disturbance plus bias, and was originally defined as the core rate on the economy's long-run growth path (Cecchetti 1997; Eckstein 1981).

The supply-shock robustness of that underlying signal is supplied by the limited-influence estimators and the optimally trimmed means (Bryan and Cecchetti 1994; Bryan, Cecchetti, and Wiggins 1997), and the core component is identified as the part of measured inflation with no long-run effect on real output (Quah and Vahey 1995). The trend extracted from the same series by the unobserved-components stochastic-volatility model is the slow-moving inflation objective against which policy is calibrated (Stock and Watson 2007).

Because the level is seasonally adjusted at source, its month-on-month change is read directly as a rate of price change rather than only against a year-earlier comparison, and reading it beside the unadjusted convention separates the within-year pattern from the underlying move. Both readings rest on the reasoning that lets a single consumer price level anchor expectations across the economy (Diewert 2002), and on the exact and superlative aggregators that define what such a level is (Diewert 1976).

For asset pricing the consumer price level is the deflator that converts nominal cash flows into real terms, and index-number theory formalizes this operation through the time- and factor-reversal tests that a deflator should satisfy (Fisher 1922). The base-quantity weights, their current-weighted dual, and the expenditure-share log-change form bound the deflation error (Laspeyres 1871; Paasche 1874; Törnqvist 1936).

Inflation-linked bonds, inflation swaps, and breakeven quotes settle on the realized path of the all-items basket, and the substitution and quality-change wedge attributed to a fixed-base index is priced into the basis between indexed and nominal instruments (Diewert 1998; Boskin et al. 1996). Such contracts reference the unadjusted vintage of that basket rather than the adjusted level served here, so the two conventions are kept apart in any settlement calculation.

What a contract settles on is therefore the published fixed-basket level and not the superlative cost-of-living target that level approximates, and that distinction is what the index-number literature makes precise (Diewert 1976, 2002). Axiomatic consistency governs whether successive vintages chain coherently for settlement (Balk 1995).

For relative-value and macro positioning the persistent component matters more than the monthly print, so the adjusted level is read against the underlying-inflation gauges and the extracted trend (Cecchetti 1997; Bryan and Cecchetti 1994; Stock and Watson 2007). The cost-of-living anchor frames the long-horizon real-return target (Konüs 1939).

USCPISA is published as a seasonally-adjusted monthly index level of all-items consumer prices, and the statistical object is that published level, expected to be integrated of order one. The sample is 953 monthly observations spanning 1947-01-01 to 2026-06-01, and the unit-root triplet is fitted on the level with a constant and trend.

The augmented Dickey-Fuller regression of Dickey and Fuller (1979), in the lag-augmented form of Said and Dickey (1984) with lag length set as in Ng and Perron (2001), does not reject the unit root with a statistic of −1.0053 at p = 0.9434, the nonparametric test of Phillips and Perron (1988) concurs with a statistic of −0.2216 at p = 0.9911, and the stationarity-null test rejects trend stationarity with a statistic of 0.9336 at p < 0.01 (Kwiatkowski et al. 1992), so the three procedures concur on a clean I(1) classification. The GLS-detrended escalation of Elliott, Rothenberg, and Stock (1996) is reserved for ambiguous outcomes and is not required on this clean reading.

On a clean integrated reading the level is not the stationary object, so the portmanteau and the break search are run on the first difference, since a level portmanteau reads the near-unit autocorrelation of a stochastic trend and a level mean-break search spuriously segments it (Perron 1989; Hamilton 2018; Bai and Perron 1998). The portmanteau statistic of Ljung and Box (1978), refining the form of Box and Pierce (1970), rejects the white-noise null on the differenced level at lags 12 and 24, with Q = 1153.13 and Q = 1635.3 and p = 0.000 in both cases. The multiple-break procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003), locates two mean shifts in the differenced series, at 1973-02-01 and 2014-08-01.

The index is seasonally adjusted at source, so under the platform convention whatever the seasonal battery detects is attributed to that adjustment and its revisions and is never presented as a KRED discovery (Ghysels and Osborn 2001). The seasonal-unit-root test of Hylleberg et al. (1990), with the monthly mechanics of Beaulieu and Miron (1993), is run on the level and rejects unit roots at the seasonal frequencies with a statistic of 5018.2469 at p = 0.000, so any seasonal signal that survives the adjustment is deterministic rather than stochastic. The seasonal portmanteau leg is the cumulative statistic through lag 24 on the first difference, 1635.301, numerically the lag-24 rung already reported rather than an independent second test, and it rejects the no-autocorrelation null at p = 0.000, while the joint test of monthly dummies on the first difference does not reject, with F = 0.9997 at p = 0.444475. The battery therefore disagrees with the adjusted designation the series carries, and the disagreement is stated as it stands, the series being neither declared seasonally clean nor credited with a newly found seasonal pattern. The reverse-null seasonal-stationarity test of Canova and Hansen (1995) is optional under the matrix and was not computed for this member.