KOSPI Composite Index

These raw equity-market series are levels recorded without transformation, namely the composite price index of a broad basket of listed shares and the aggregate market value of that same basket, each carried at the level at which it is disseminated in the organized secondary market. A composite index is a value-weighted index number that compresses the prices of many constituent shares into a single figure read against a base-period reference, and the market capitalization is the summed current value of the same listed universe.

What such an aggregate measures is fixed by index-number choices. A base-period-weighted aggregation fixes the reference basket (Laspeyres 1871), a current-weighted aggregation lets the weights move with outstanding value (Paasche 1874), and the geometric reconciliation of the two satisfies the reversal tests that discipline any index (Fisher 1922). The share-weighted log-change form and the exact-and-superlative classification set out which formulas track an underlying aggregator (Törnqvist 1936; Diewert 1976), the atomistic-versus-functional systematization fixes the chain-versus-fixed-base choice (Frisch 1936), and the continuous-time limit underlies chain-linked value aggregation (Divisia 1925). A market-value aggregate is in this sense a level of aggregate valuation of the kind that national-accounting practice also sums (Kuznets 1941).

Read as a business barometer, the equity aggregate is the constituent series that a composite index of aggregate conditions has long incorporated (Persons 1923), classified among the leading rather than the coincident measures (Mitchell and Burns 1938; Burns and Mitchell 1946), and the joint movement of yields and share prices is documented in the same tradition (Macaulay 1938). KRED retains the disseminated level itself rather than any re-aggregation of it.

KRED applies no transformation to these series and enters each equity-market level at the figure recorded on the business day it is published. It imposes no rescaling, deflation, splicing, smoothing, or annualization, and performs no re-weighting, re-basing, or filtering. The measurement basis is the aggregation convention by which a composite index and a market-value total come to exist, a value-weighted sum of constituent share prices carried against a fixed base, the elemental figure that sits prior to any further index-number step.

The construction methodology that would build such an aggregate from its constituents is documented across the index-number literature, yet KRED records the disseminated figure ahead of all of it. The base-period and current-period weighting schemes are the two poles of aggregation (Laspeyres 1871; Paasche 1874), the reversal-test and exact-index apparatus fixes which weighted mean is admissible (Fisher 1922; Diewert 1976), the log-change superlative form and the axiomatic characterization catalogue the admissible formulas (Törnqvist 1936; Balk 1995), and the chain-versus-fixed-base and chain-linking choices govern how a level is carried through time (Frisch 1936; Hill 1988; Divisia 1925).

The composite-indicator methodology that would instead read the aggregate as a cyclical signal is likewise external to the stored figure, namely the standardization-and-detrending assembly of many activity series (Persons 1923), the programmed turning-point and diffusion construction (Bry and Boschan 1971; Moore 1961), and the single-index state-of-the-economy recasting (Stock and Watson 1989), none of which KRED performs on the level it retains.

Economically the equity aggregate is read as a forward-looking barometer of business conditions. Share prices embed discounted expectations of future earnings, so the composite level tends to turn ahead of the reference cycle and has long been grouped among the leading indicators (Mitchell and Burns 1938; Burns and Mitchell 1946). The construction of a composite index of aggregate conditions from many such series was set out early (Persons 1923), the diffusion and composite apparatus that formalizes it was codified (Moore 1961; Shiskin 1961), and the indicator approach was synthesized and evaluated for its measurement and forecasting record (Zarnowitz 1992).

The interpretive caution that measurement without an explicit model can mislead applies squarely to reading a cyclical signal off the level (Koopmans 1947), and the single-index dynamic-factor recasting supplies the modern statistical footing for treating the aggregate as a state of the economy (Stock and Watson 1989). The joint movement of yields and share prices places the equity level alongside the interest-rate cycle in the same empirical tradition (Macaulay 1938).

As a valuation aggregate the market-value total is a level of the kind that national-accounting practice sums into economy-wide totals (Kuznets 1941; Fabricant 1940), and the index-number reasoning that fixes what a weighted aggregate of prices can and cannot say bounds the economic content that a single composite level carries (Fisher 1922; Diewert 1976).

In financial use the recorded level is the settlement and mark-to-market reference for the instruments written on the equity aggregate, so that index futures, options, and passive funds are valued directly against this figure and portfolio performance is benchmarked to it. The market-value total is the free-float base from which index weights and capitalization-based allocations are computed, an aggregate valuation of the listed universe of the kind long summed in aggregate-value accounting (Kuznets 1941).

The index-number apparatus governs how constituent prices are compounded into the traded benchmark, so the base-weighted, current-weighted, and reversal-test-consistent constructions determine what a derivative on the level actually tracks (Laspeyres 1871; Paasche 1874; Fisher 1922; Diewert 1976). The chain-linking and re-basing conventions that carry a benchmark through corporate actions and constituent turnover are documented in the same literature (Frisch 1936; Hill 1988; Divisia 1925).

Because the level leads the cycle, it also serves as a market-based conditioning variable for risk and allocation, read through the leading-indicator and turning-point tradition that dates and interprets its swings (Persons 1923; Mitchell and Burns 1938; Moore 1961; Zarnowitz 1992). The joint behavior of yields and share prices frames the equity level within cross-asset positioning (Macaulay 1938).

On the 7,966 daily observations spanning 1995-01-03 to 2026-07-03, fit with a constant and trend, the unit-root battery agrees that the composite equity index is integrated of order one. The augmented Dickey-Fuller test of Dickey and Fuller (1979), in the ARMA-consistent lag-augmented form of Said and Dickey (1984) and with lag length set as in Ng and Perron (2001), does not reject a unit root with p = 1.0000, the nonparametric Phillips and Perron (1988) test concurs with p = 1.0000, and the Kwiatkowski et al. (1992) stationarity test rejects its trend-stationary null at p < 0.01, so the verdict is an unambiguous I(1). The GLS-detrended power escalation of Elliott, Rothenberg, and Stock (1996) is reserved for ambiguous outcomes under the house protocol and is not required on this clean reading.

Because the level is integrated, the mean-shift and serial-correlation diagnostics are run on the first difference, the stationary object those procedures require, since a break search or a portmanteau on an integrated level would spuriously segment and read near-unit autocorrelations (Bai and Perron 1998; Perron 1989). The multiple-break procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003), finds no break in the mean of the differenced series, consistent with the parameter-instability inference of Andrews (1993). The Ljung and Box (1978) portmanteau statistic, refining the original Box and Pierce (1970) form, is computed on the first difference and rejects the white-noise null at lags 10 and 20, with Q = 398.67 and Q = 814.30 and p = 0.000 and p = 0.000, and the automatic portmanteau test of Escanciano and Lobato (2009) does not detect further dependence with a statistic of 0.51 at p = 0.476.

The series is daily and has no low-integer seasonal period, so the seasonal-unit-root machinery of Hylleberg et al. (1990) and the Canova and Hansen (1995) seasonal-stationarity test are inapplicable and are deliberately not run, the degeneracy of the seasonal auxiliary regression at a daily period being the standard ground (Beaulieu and Miron 1992; Ghysels and Osborn 2001).