South Korea Retail Sales Index (SA)

KRRETAIL is a monthly index number that measures the volume of goods sold through retail trade relative to a base period set to 100. It is a seasonally adjusted retail sales index recorded as ingested without transformation, and KRED applies no reprocessing to it.

As an index of physical sales volume, this series belongs to the family of quantity indices resting on axiomatic and chain foundations (Fisher 1922; Frisch 1936; Diewert 1976). The fixed-weight aggregation rule and its current-weighted counterpart bound the unobserved true index from above and below (Laspeyres 1871; Paasche 1874).

The aggregation of differently measured quantity components is expressed in a continuous-time form and a share-weighted log-change form (Divisia 1925; Törnqvist 1936).

This series sits inside the boundary of production-and-expenditure accounting and reads as part of the output and expenditure measures that those accounting conventions define (Kuznets 1941; Stone 1947; Meade and Stone 1941). Within the comovement tradition of activity series and the composite-conditions construction it is one component series (Burns and Mitchell 1946; Persons 1923).

The annual chain-linking of volume measures and the physical-output deflation logic form the basis on which this index is produced (Hill 1988; Fabricant 1940). A rise in the index means the physical volume of goods sold through retail has increased by that much.

KRED applies no transformation to this monthly index and stores it exactly as recorded, performing none of rescaling, deflating, smoothing, or annualizing. Because the underlying series is itself seasonally adjusted at source before ingestion, KRED performs no further filtering and carries the published level across unchanged.

The measurement basis by which the number comes to exist is the index-number framework. A quantity relative for each retail category is weighted and aggregated under the fixed-base rule or the current-weighted rule, and the two rules bound the ideal index from above and below (Laspeyres 1871; Paasche 1874). Fisher (1922) singles out that ideal index through the axiomatic test approach, and Frisch (1936) systematizes it across the chain-versus-fixed-base problem.

Modern practice replaces fixed weights with the annual chain-linking of volume measures (Hill 1988), and it uses the translog index shown to be exact for flexible aggregators (Diewert 1976). This translog form holds identically whether as a continuous-time aggregate or a share-weighted log-change (Divisia 1925; Törnqvist 1936).

The quantity relatives rest on the physical-output deflation logic (Fabricant 1940). The resulting volume series respects the production-and-expenditure boundary and the netting conventions (Kuznets 1941; Stone 1947; Meade and Stone 1941), and the estimate carries formalized reliability bounds (Stone, Champernowne, and Meade 1942).

Retail sales volume is a high-frequency reading on household consumption demand and the consumer-spending side of aggregate activity. The series therefore enters production-income-expenditure accounting as a monthly proxy for the consumption component of the expenditure measure of output (Kuznets 1941; Stone 1947; Meade and Stone 1941).

Within the reference-cycle tradition the series is one of the comoving activity indicators whose turning points help date expansions and contractions (Burns and Mitchell 1946). In the composite-conditions construction it is a standardized building block of an aggregate business-conditions index (Persons 1923).

Read as a chain volume measure, real retail sales strip price change out of nominal turnover so that movements reflect quantities bought (Hill 1988; Diewert 1976). This is the same physical-output reasoning applied to manufacturing (Fabricant 1940).

The index-number basis lets the level be compared across periods (Fisher 1922; Laspeyres 1871; Paasche 1874; Frisch 1936). The reliability bounds caution that month-to-month moves are estimates rather than exact counts (Stone, Champernowne, and Meade 1942).

For markets the retail sales index is a coincident gauge of consumption momentum that conditions expectations for monetary policy, consumer-facing earnings, and the cyclical components of fixed income and equity. This reading is made within the reference-cycle framework and the composite-conditions logic (Burns and Mitchell 1946; Persons 1923).

Because it is a chain volume measure, real retail sales separate quantity from price so that a surprise in the index speaks to demand rather than inflation (Hill 1988; Diewert 1976). This complements the physical-output reading (Fabricant 1940).

Its place inside the expenditure accounts lets desks map the print onto the consumption share of output (Kuznets 1941; Stone 1947; Meade and Stone 1941). The index-number construction governs how revisions and rebasing shift the level (Fisher 1922; Laspeyres 1871; Paasche 1874; Frisch 1936; Divisia 1925; Törnqvist 1936).

The reliability bounds warn against over-trading a single noisy monthly print (Stone, Champernowne, and Meade 1942).

KRRETAIL is a seasonally-adjusted-at-source retail-sales index, and its published level is the statistical object whose integration order the triplet assesses. The sample is 376 monthly observations spanning 1995-01 to 2026-04, and the tests are fitted 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), fails to reject the unit root at p = 0.507, and the stationarity-null test rejects trend stationarity at p = 0.012 (Kwiatkowski et al. 1992), so the augmented Dickey-Fuller and KPSS legs concur toward an I(1) reading. The nonparametric test of Phillips and Perron (1988) is the sole dissenter, rejecting the unit root at p = 0.0008, which is the documented Phillips-Perron over-rejection toward spurious stationarity under near-unit moving-average errors (Ng and Perron 2001), so no clean order of integration is assigned. The GLS-detrended escalation of Elliott, Rothenberg, and Stock (1996), run only as confirmation of the augmented Dickey-Fuller leg, fails to reject at p = 0.158 and corroborates that leg without upgrading the ambiguous verdict.

Because the level is not a clean stationary object, the portmanteau and the break search are run on its first difference, since a level portmanteau reads mechanical near-unit autocorrelation and a level mean-break search spuriously segments the series (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 series at p = 0.000, while the multiple-break procedure computed by the dynamic-programming algorithm of Bai and Perron (2003) finds no break in the mean of the differenced series.

The seasonal battery is run with the interpretation that any absence of seasonality reflects the source adjustment rather than an inherent property. The seasonal-unit-root test of Hylleberg et al. (1990), with the monthly mechanics of Beaulieu and Miron (1993), rejects unit roots at the seasonal frequencies at p = 0.000, and the seasonal dummies are not jointly significant at p = 0.437, so no deterministic seasonality survives, which reflects the seasonal adjustment already applied at source and not an inherent absence of a seasonal pattern, consistent with the stationary-seasonality reading of Canova and Hansen (1995) and the seasonal-adjustment literature (Ghysels and Osborn 2001).