Univariate detrending methods with stochastic trends

This paper discusses detrending economic time series, when the trend is modelled as a stochastic process. It considers unobserved components models in which the observed series is decomposed into a trend (a random walk with drift) and a residual stationary component. Optimal detrending methods are discussed, as well as problems associated with using these detrended data in regression models. The methods are applied to three time series: GNP, disposable income, and consumption expenditures. The detrended data are used to test a version of the Life Cycle consumption model.     

The Information Content of Cash Flows and the Random Walk: Evidence from the Helsinki Stock Exchange

Using a sample from the Helsinki Stock Exchange, this paper examines whether observed market reactions to unexpected cash flows are sensitive to the random walk assumption of cash flow behaviour. We consider the random walk (with drift) model commonly used in related literature, and we consider cash flow expectations generated with individually estimated parsimonious univariate time series models and an index model. Market reactions to unexpected cash flows are indiscernible under the random walk assumption, while significant market reactions are found when expectations of cash flows are measured with models which better capture their time series properties. Prior studies that rely on the random walk assumption have probably been biased against finding a significant market reaction to cash flow information.     

Market Dependence and Economic Events

Recent studies on stock market pricing have rejected the random walk model for short-term periods and have concentrated on long-term persistent or mean-reverting dependence. The problem with these studies is that their statistical results can be biased by the shorter term dependence. Rather than trying to develop a unified theory that explains both short- and long-term dependence, current studies use different methodologies to correct for the short-term dependence while trying to test for long-term dependence. This paper uses a sequential information theory to focus attention on short-term dependence effects. This theory states that the market process is a nonstationary mean process surrounded by a nonstationary autocovariance error process. A nonstationary mean process implies short-term dependence resulting from changing economic events (new information). Long-term persistent dependence then derives from nonperiodic economic cycles. A new empirical approach, a cross-sectional autocorrelation coefficient is used since it is free from the stationarity problems of previous techniques.     

RESIDUAL INCOME,REVERSIBILITY AND THE VALUATION OF EQUITY

Using a continuous time reformulation of the Garman & Ohlson (1980) equity valuation model, we show that the linear pricing technologies, which characterize this area of accounting research, are special cases of a more general non-linear pricing relationship. These non-linearities arise from the fact that firms have the option of terminating their production and investment plans, especially if they turn out to be ‘significant’ loss-making ventures. We demonstrate the potential significance of these non-linearities for a parsimonious interpretation of the Ohlson (1995) model based on the assumption that the firm’s residual income stream is generated by the Student distributions of Praetz (1972) and Blattberg & Gonedes (1974). These processes are based on the assumption that the residual income variable is generated by an elastic (or mean reverting) random walk whose increments have a variance that depends on its current instantaneous value. Since several other well-known processes are nested within the Student distributions (e.g. random walk, Ornstein–Uhlenbeck process), they are a very useful set of distributions through which to demonstrate the potential impact of non-linearities on the pricing relationships of this area.     

A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the ‘business cycle’

This paper introduces a general procedure for decomposition of non-stationary time series into a permanent and transitory component allowing both components to be stochastic. The permanent component is shown to be a random walk with drift and the transitory or cyclical component is a stationary process with mean zero. The decomposition methodology, which depends only on past data and therefore is computable in ‘real time’, is applied to the problem of measuring and dating business ‘cycles’ in the portwar U.S. economy. We find that measured expansions and contractions are of roughly equivalent duration and that our dating of cyclical episodes tends to lead the traditional NBER dating and, to a lesser extent, the ‘growth cycle’ chronology of Zarnowitz and Boschan (1977).     

Random walk and monetary causality in five exchange markets

Time series behavior of monthly spot exchange rates for the French franc, the Deutsche mark, the Italian lira, the Japanese yen, and the UK pound, all priced in relation to the US dollar, shows the robustness of the random walk hypothesis. Incremental efficiency is investigated by a new test procedure, based on the reduction of the forecast error variance, which is a direct implementation of the definition of Granger causality. Exchange markets are found to be not only money efficient, but also monetary efficient in that they are efficient with respect to real income and market interest rates in addition to money stock.     

Stochastic simulations of time series within Weierstrass–Mandelbrot walks

Abstract

In the present work we extend Lévy walks to allow the velocity of the walker to vary. We call these extended Lévy walks Weierstrass-Mandelbrot walks. This is a generalized model of the Lévy walk type which is still able to describe both stationary and non-stationary stochastic time series by treating the initial step of the walker differently. The model was partly motivated by the properties of financial time series and tested on empirical data extracted from the Warsaw stock exchange since it offers an opportunity to study in an unbiased way several features of the stock exchange in its early stages. We extended the continuous-time random walk formalism but the (generalized) waiting-time distribution (WTD) and sojourn probability density still play a fundamental role. We considered a one-dimensional, non-Brownian random walk where the walker moves, in general, with a velocity that assumes a different constant value between the successive turning points, i.e. the velocity is a piecewise constant function. So far the models which have been developed take only one chosen value of this velocity into account and therefore are unable to consider more realistic stochastic time series. Moreover, our model is a kind of Lévy walk where we assume a hierarchical, self-similar in the stochastic sense, spatio-temporal representation of WTD and sojourn probability density. The Weierstrass-Mandelbrot walk model makes it possible to analyse both the structure of the Hurst exponent and the power-law behaviour of kurtosis. This structure results from the hierarchical, spatio-temporal coupling between the walker displacement and the corresponding time of the walks. The analysis makes use of both the fractional diffusion and the super-Burnett coefficients. We constructed the diffusion phase diagram which distinguishes regions occupied by classes of different universality. We study only such classes which are characteristic of stationary situations. We proved that even after taking a moving averaging of the stochastic time series which makes results stationary in the sense that they are independent of the beginning moment of the random walk, it is still possible to see the non-Gaussian features of the basic stochastic process. We thus have a model ready for describing data presented, e.g., in the form of moving averages. This operation is often used for stochastic time series, especially financial ones. Based on the hierarchical representation of WTD we introduce an efficient Monte Carlo algorithm which makes a numerical simulation of individual runs of stochastic time series possible; this facilitates the study of empirical stochastic time series.     

Asymptotic analysis of the ruin with stationary stable steps generated by dissipative flows

We study the exceedance probability of a high threshold (ruin probability) for a random walk with a negative linear drift, where the steps of the walk (claim sizes) constitute a stationary ergodic symmetric α-stable process. We casually use the language of insurance, although this is a popular problem in many other fields of applied probability as well. We refer to ergodic theory to split the step process into two independent processes. We focus on the processes generated by dissipative flows, which are known to have a mixed moving average representation, and we restrict our attention to regular moving averages with non-negative kernels. We give results for the order of magnitude of the exceedance probability as the threshold goes to infinity in the cases of discrete-time and continuous-time claim processes.     

Investment intensity of currencies and the random walk hypothesis: Cross-currency evidence

This paper studies the cross-currency and temporal variations in the random walk behavior in exchange rates. We characterize currencies with relatively large investment flows as investment intensive and conjecture that the more investment intensive a currency is, the closer its exchange rate adheres to random walk. Using 29 floating bilateral USD exchange rates, we find that the higher the investment intensity, the less likely it is to reject random walk and the smaller the deviation from random walk is. However, the effect of investment intensity is non-monotonic. Application of threshold models shows that after investment intensity reaches the estimated thresholds, the level of investment intensity has no further effect on the deviation from random walk. These findings help reconcile the previous conflicting results on the random walk in exchange rates by focusing on the effect of cross-currency and temporal variations in investment intensity.     

UK Housing Market: Time Series Processes with Independent and Identically Distributed Residuals

The paper examines whether a univariate data generating process can be identified which explains the data by having residuals that are independent and identically distributed, as verified by the BDS test. The stationary first differenced natural log quarterly house price index is regressed, initially with a constant variance and then with a conditional variance. The only regression function that produces independent and identically distributed standardised residuals is a mean process based on a pure random walk format with Exponential GARCH in mean for the conditional variance. There is an indication of an asymmetric volatility feedback effect but higher frequency data is required to confirm this. There could be scope for forecasting the index but this is tempered by the reduction in the power of the BDS test if there is a non-linear conditional variance process.     

Does the exchange rate follow a random walk? A Monte Carlo study of four tests for a random walk

Several authors have urged that real and nominal exchange rates follow a random walk. Conditions under which the exchange rate follows a random walk are reviewed in this paper. Many of these do not appear to hold. Therefore, the empirical evidence presents a puzzle : some evidence suggets the exchange rate follows a random walk, while other evidence suggests the opposite should be true. This paper attempts to reconcile the evidence. It is argued that the tests for a random walk have low power. Monte Carlo evidence on four tests for a random walk, is presented that suppors this claim.     

Housing Price Dynamics in Time and Space: Predictability,Liquidity and Investor Returns

It is widely accepted that aggregate housing prices are predictable, but that excess returns to investors are precluded by the transactions costs of buying and selling property. We examine this issue using a unique data set—all private condominium transactions in Singapore during an eleven-year period. We model directly the price discovery process for individual dwellings. Our empirical results clearly reject a random walk in prices, supporting mean reversion in housing prices and diffusion of innovations over space. We find that, when house prices and aggregate returns are computed from models that erroneously assume a random walk and spatial independence, they are strongly autocorrelated. However, when they are calculated from the appropriate model, predictability in prices and in investment returns is completely absent. We show that this is due to the illiquid nature of housing transactions. We also conduct extensive simulations, over different time horizons and with different investment rules, testing whether better information on housing price dynamics leads to superior investment performance.     

Purchasing power parity: Modeling and testing mean reversion

A model of mean reversion of exchange rates to purchasing power parity is developed and tested where exchange rates are assumed to follow a mean reverting elastic random walk toward a stochastic PPP rate. The model recognizes the possibility that mean reversion towards PPP may be nonlinear which allows greater flexibility in the adjustment process. Regression equations consistent with the theoretical model are derived. The model is tested using long- and short-term data for six countries. While the results are generally consistent with the findings of previous studies, evidence is presented which demonstrates that the mean reversion process is not linear for some countries.     

A new perspective on post‐earnings‐announcement‐drift: Using a relative drift measure

Prior research finds that there is a delayed reaction to both analyst‐based earnings surprises and random‐walk‐based earnings surprises. Focusing on the market reaction from the post‐announcement window, prior studies show that analyst‐based drift is larger than random walk‐based drift. This finding is counter‐intuitive if we believe large, sophisticated investors tend to trade on analysts’ forecast earnings news and thus react faster and more completely than smaller and less sophisticated investors react to random walk earnings news. In this study, we construct a relative measure of post‐earnings‐announcement drift (PEAD) (i.e., drift as a proportion of total market reaction to earnings news) which we refer to as the ‘drift ratio’, and we provide evidence, consistent with our intuition, that analyst‐based drift ratio is smaller (not greater) than random‐walk‐based drift ratio. We find that this difference is more pronounced in more recent periods and for firms with more sophisticated investors. Our approach to measure the PEAD is more intuitive than that in traditional PEAD literature. Our results thus complement existing research findings by utilizing the drift ratio measure to generate new insights about the drift phenomenon.     

The Components of Accounting Ratios as Co-integrated Variables

Time series of accounting variables may often be non-stationary, i.e. they have a unit root, as in the common example of a random walk. This can lead to spurious results in time series regression analysis which uses such variables. The problem is overcome if the variables are co-integrated. This paper examines and tests the proposition that, where the variables are expressed in logarithmic form, calculating a ratio may capture the effects of co-integration. Thus, accounting ratios (calculated in logarithmic form) might be stationary, and therefore exempt from the econometric pathology associated with their component variables.     

Why Do Analysts use a Zero Forecast for Other Comprehensive Income?

Accounting theory and accounting researchers stress the importance of clean surplus accounting and comprehensive income to corporate valuation. However, casual observation suggests that sell-side equity analysts routinely ignore other comprehensive income (OCI) in their forecasts and instead focus on forecasting earnings (before OCI). Using a sample of analyst reports, I first confirm that analysts normally omit forecasts of OCI or comprehensive income from their reports, consistent with analysts forecasting OCI as zero. I then predict and find that a zero forecast for OCI generally produces lower forecasting errors than alternative time-series models, such as a random walk or AR(1) model, suggesting a rational reason why analysts take this approach. Finally, I predict and find that although analysts’ point forecasts of future OCI are usually zero, their implied cost of equity estimates are consistent with analysts forecasting a positive variance for OCI.     

Variance ratio tests of the random walk hypothesis for European emerging stock markets

The hypothesis that stock market price indices follow a random walk is tested for five European emerging markets, Greece, Hungary, Poland, Portugal and Turkey, using the multiple variance ratio test. In four of the markets, the random walk hypothesis is rejected because of autocorrelation in returns. For the Istanbul market, which had markedly higher turnover than the other markets in the 1990s, the stock price index follows a random walk. This contrasts with the results of earlier research, carried out for periods of lower turnover, which rejected the random walk hypothesis.     

Purchasing Power Parity in the Long Run

This paper re-examines the evidence on Purchasing Power Parity (PPP) in the long run. Previous studies have generally been unable to reject the hypothesis that the real exchange rate follows a random walk. If true, this implies that PPP does not hold. In contrast, this paper casts serious doubt on this random walk hypothesis. The results follow from more powerful estimation techniques, applied in a multilateral framework. Deviations from PPP, while substantial in the short run, appear to take about three years to be reduced in half.     

The information content of security prices

The study derives a relationship between prices changes and earnings changes by expanding the information upon which earnings expectations are conditioned to include data other than prior earnings history. In particular, price is used as a surrogate for additional information available to market participants. This relationship provides an interpretation of the contemporaneous association between price changes and earnings changes previously observed by Ball and Brown (1968) and Beaver, Clarke and Wright (1979), among others. It also provides a basis for inferring from prices the earnings process and the expected future earnings as perceived by market participants. In doing so, it inverts the familiar price-earnings relationship and uses price as a predictor of earnings. The study differs from previous research which has examined the time series behavior of earnings based solely on previous earnings realizations. This approach can potentially lead to earnings forecasting models that are more accurate than the random walk with a drift that has been robust against challengers. In particular, the evidence indicates that security prices behave as if earnings are perceived to be dramatically different from a simple random walk process. Preliminary evidence also indicates that price-based forecasting models are more accurate than the random walk with a drift model.     

Where is the GE? Consumption Dynamics in DSGEs

We offer a partial equilibrium perspective on the behavior of consumption in dynamic stochastic general equilibrium (DSGE) models. We consider a benchmark dynamic general equilibrium model and show that a standard calibration implies that the real interest rate is essentially fixed. One manifestation of this feature is that, with separable preferences, the reaction of consumption to total factor productivity (TFP) shocks is flat: the random‐walk permanent income hypothesis holds almost exactly, pretty much as in a partial equilibrium consumption‐savings problem. These results help explain the prominent role of aggregate demand, and how it is achieved, in modern DSGE analysis.