Seasonal Random Walk Research Articles

Can we profit from BigTechs' time series models in predicting earnings per share? Evidence from Poland

<abstract> <p>Forecasting earnings for publicly traded companies is of paramount significance for investments, which is the background of this research. This holds particularly true in emerging markets where the coverage of these companies by financial analysts' predictions is limited. This research investigation delves into the prediction inaccuracies of cutting-edge time series forecasting algorithms created by major technology companies such as Facebook, LinkedIn, Amazon, and Google. These techniques are employed to analyze earnings per share data for publicly traded Polish companies during the period spanning from the financial crisis to the pandemic shock. My objective was to compare prediction errors of analyzed models, using scientifically defined error measures and a series of statistical tests. The seasonal random walk model demonstrated the lowest error of prediction, which might be attributable to the overfitting of complex models.</p> </abstract>

Can exponential smoothing do better than seasonal random walk for earnings per share forecasting in Poland?

The accurate prediction of listed companies’ earnings plays a critical role in successful investing. This piece of research contrasts estimation errors of the seasonal random walk model and exponential smoothing models employed in the earnings per share (EPS) data for Polish listed businesses from the timespan between 2008–2009. The models are compared using the mean arctangent absolute percentage error (MAAPE) metric. The best model across all quarters and years is the seasonal random walk (SRW) model, when contrasted with the other models studied regardless of the analysed time spans and error metrics. Contrary to the results obtained from the US market, the more intricate exponential smoothing model, comprising a seasonal and a trend component, does not suitably explain the behaviour of Polish companies. This could be attributable to the simpler demeanour of the Polish market and the absence of a trend in the EPS data.

The modeling of earnings per share of Polish companies for the post-financial crisis period using random walk and ARIMA models

The proper forecasting of listed companies’ earnings is crucial for their appropriate pricing. This paper compares forecast errors of different univariate time-series models applied for the earnings per share (EPS) data for Polish companies from the period between the last financial crisis of 2008–2009 and the pandemic shock of 2020. The best model is the seasonal random walk (SRW) model across all quarters, which describes quite well the behavior of the Polish market compared to other analyzed models. Contrary to the findings regarding the US market, this time-series behavior is well described by the naive seasonal random walk model, whereas in the US the most adequate models are of a more sophisticated ARIMA type. Therefore, the paper demonstrates that conclusions drawn for the US might not hold for emerging economies because of the much simpler behavior of these markets that results in the absence of autoregressive and moving average parts.

Forecasting monthly soil moisture at broad spatial scales in sub-Saharan Africa using three time-series models: evidence from four decades of remotely sensed data

ABSTRACT Soil moisture is a critical environmental variable that determines primary productivity and contributes to climatic processes. It is, therefore, important to forecast soil moisture to inform expectations of derivative outputs reliably. While forecasting soil moisture continues to advance, there is a need to extend it to different geoclimatic regions, including in sub-Saharan Africa, where livelihoods predominantly rely on subsistence agriculture. We used remotely sensed soil moisture data produced by the European Space Agency – Climate Change Initiative (ESA CCI). The data, which covered the period 1978 to 2019, were used to forecast monthly soil moisture in different agroecological zones and land cover types. The Seasonal Random Walk, Exponential Smoothing and Seasonal Autoregressive Integrated Moving Average (SARIMA) forecasting models were trained on 70% of the data (November 1978 – August 2007) and subsequently applied to a test dataset (September 2007 – December 2019). All models showed solid prediction accuracies for all agroecological zones (unbiased root mean square error, ubRMSE ≤ 0.05 m3 m−3) and land cover types (ubRMSE ≤ 0.04 m3 m−3). This was corroborated by similarities in season-adjusted anomalies between observed and forecasted soil moisture for nearly all agroecological zones and land cover types, with a correlation coefficient of r > 0.5 for most locations). The broad-scale interpretation of soil moisture forecasting can inform moisture availability and variability by regions; however, more research is encouraged to improve forecasting at spatially and temporally detailed levels to assist small-scale farming practices in the continent.

Analysts versus time-series forecasts of quarterly earnings: A maintained hypothesis revisited

We re-examine the maintained hypothesis of analysts' quarterly earnings per share (EPS) superiority versus ARIMA time-series forecasts. While our empirical results are consistent with overall analysts' dominance, they suggest a more contextual interpretation of this important relationship. Specifically, we find that for a relatively large number of cases (approximately 40%) ARIMA time-series forecasts of quarterly EPS are equal to or more accurate than consensus analysts' forecasts. Moreover, the percentage of time-series superiority increases: (1) for longer forecast horizons, (2) as firm size decreases, and (3) for high-technology firms. Due to the data demands that ARIMA forecasting requires we also examine using a seasonal random walk (SRW) model that requires only one year of data to create quarterly forecasts. Although the ARIMA time-series model results in a significant reduction in sample size it dominates the SRW model. Our findings support the analyst dominance over time series models but suggest that ARIMA time-series models may provide useful input to researchers seeking quarterly EPS expectation models for certain types of firms.

Earnings acceleration and stock returns

We document that earnings acceleration, defined as the quarter-over-quarter change in earnings growth, has significant explanatory power for future excess returns. These excess returns are robust to a wide range of previously documented anomalies and a battery of risk controls. The future return predictability appears to be consistent with investors assuming a seasonal random walk model for quarterly earnings and missing predictable implications of earnings acceleration for future earnings growth. Finally, the excess returns from the basic earnings acceleration strategy can be enhanced further by focusing on profit firms, low earnings volatility firms and on specific patterns of earnings acceleration.

Time-Series Properties of Quarterly Aggregate Earnings

This analysis examines the time-series properties of quarterly aggregate earnings. We find that when aggregated, quarterly earnings can be fairly well described as following a simple random walk (RW) process. That is, the best historical time-series predictor for quarterly aggregated earnings is aggregated earnings from the prior quarter and this specification, in particular, outperforms a seasonal random walk (SRW) specification. Hence, unlike firm level earnings, the seasonal earnings lag is not the best single value predictor for aggregate earnings. When we consider more complicated multi-variable RW changes specifications, we find that the use of first or second order autocorrelation provides some improvement in specification. Finally, drawing on prior work by Sadka and Sadka (2009), we demonstrate the empirical relevance of the choice between an RW and an SRW “surprise” specification by identifying substantive differences in how each is predicted by lagged market returns.

Statistical and economic evaluation of time series models for forecasting arrivals at call centers

Call centers' managers are interested in obtaining accurate point and distributional forecasts of call arrivals in order to achieve an optimal balance between service quality and operating costs. We present a strategy for selecting forecast models of call arrivals which is based on three pillars: (i) flexibility of the loss function; (ii) statistical evaluation of forecast accuracy; (iii) economic evaluation of forecast performance using money metrics. We implement fourteen time series models and seven forecast combination schemes on three series of daily call arrivals. Although we focus mainly on point forecasts, we also analyze density forecast evaluation. We show that second moments modeling is important both for point and density forecasting and that the simple Seasonal Random Walk model is always outperformed by more general specifications. Our results suggest that call center managers should invest in the use of forecast models which describe both first and second moments of call arrivals.

Earnings Acceleration and Stock Returns

We document that earnings acceleration, defined as the quarter-over-quarter change in earnings growth, has significant explanatory power for future excess returns. These excess returns are robust to a wide range of previously documented anomalies as well as a battery of risk controls. The magnitude of the excess returns (1.8% in a month-long window) is comparable to those from book-to-market, post-earnings announcement drift and gross profitability anomalies. The future return predictability appears to be consistent with investors assuming a seasonal random walk model for quarterly earnings and missing predictable implications of earnings acceleration for earnings growth two and three quarters hence. Finally, the excess returns from the basic earnings acceleration trading strategy can be enhanced further by nearly 45% by focusing on specific patterns of earnings acceleration.

Statistical and Economic Evaluation of Time Series Models for Forecasting Arrivals at Call Centers

Call centers' managers are interested in obtaining accurate forecasts of call arrivals because these are a key input in staffing and scheduling decisions. Therefore their ability to achieve an optimal balance between service quality and operating costs ultimately hinges on forecast accuracy. We present a strategy to model selection in call centers which is based on three pillars: (i) a flexible loss function; (ii) statistical evaluation of forecast accuracy; (iii) economic evaluation of forecast performance using money metrics. We implement fourteen time series models and seven forecast combination schemes on three series of call arrivals. We show that second moment modeling is important when forecasting call arrivals. From the point of view of a call center manager, our results indicate that outsourcing the development of a forecasting model is worth its cost, since the simple Seasonal Random Walk model is always outperformed by other, relatively more sophisticated, specifications.

Illuminating ARIMA model-based seasonal adjustment with three fundamental seasonal models

Our starting place is the first order seasonal autoregressive model. Its series are shown to have canonical model-based decompositions whose finite-sample estimates, filters, and error covariances have simple revealing formulas from basic linear regression. We obtain analogous formulas for seasonal random walks, extending some of the results of Maravall and Pierce (J Time Series Anal, 8:177–293, 1987). The seasonal decomposition filters of the biannual seasonal random walk have formulas that explicitly reveal which deterministic functions they annihilate and which they reproduce, directly illustrating very general results of Bell (J Off Stat, 28:441–461, 2012; Center for Statistical Research and Methodology, Research Report Series, Statistics #2015-03, U.S. Census Bureau, Washington, D.C. https://www.census.gov/srd/papers/pdf/RRS2015-03, 2015). Other formulas express phenomena heretofore lacking such concrete expression, such as the much discussed negative autocorrelation at the first seasonal lag quite often observed in differenced seasonally adjusted series. An innovation that is also applied to airline model seasonal decompositions is the effective use of signs of lag one and first-seasonal-lag autocorrelations (after differencing) to indicate, in a formal way, where smoothness is increased by seasonal adjustment and where its effect is opposite.

Time-series Models Forecasting Performance in the Baltic Stock Market

Contradicting evidence on time-series and financial analysts’ forecasting performance calls for further research in emerging markets. Motivation to use time-series models rather than analysts’ forecasts stems from recent research that reports time-series predictions to be superior to analysts’ forecasts in predicting earnings for longer periods and for small firms that are hardly followed by financial analysts, especially in emerging markets. The paper aims to explore time-series models performance in forecasting quarterly earnings for Baltic Firms in 2000-2009. The paper uses simple and seasonal random walk models with and without drift, Foster’s, Brown-Rozeff’s and Griffin-Watts’ models to forecast quarterly earnings. It also employs the firm-specific Box-Jenkins methodology to perform time-series analysis for individual firms. Forecasting performance of selected models is compared on the basis of goodness-of-fit statistics. The paper finds that naive time-series models outperform premier ARIMA family models in terms of mean percentage errors and average ranks. The findings suggest that investors use naive models to form their expectations.

The impact of accruals and lines of business on analysts’ earnings forecast superiority

In this paper, we examine the linkage between analyst advantage (AA) (compared to the seasonal random walk model) in the prediction of quarterly earnings-per-share (EPS) and a broad set of economic determinants. Specifically, we employ a pooled cross-sectional time-series regression model where AA is linked to a set of firm-specific economic determinants that have been employed in extant work (e.g., Brown et al. in J Account Res 22:49–67, 1987; Kross et al. in Account Rev 65:461–476, 1990). We refine this set of independent variables by including a new variable (RATIODEV) based upon Sloan (Account Rev 71(3):289–315, 1996) who documents that differential levels of accruals impact future earnings performance. This variable is particularly salient in explaining AA since analysts may be in a position to identify the permanent component of accruals via fundamental financial analysis. Additionally, we refine the measurement of lines of business—consistent with the reporting requirements of SFAS No. 131 relative to extant work that operationalized proxies for this variable based upon SFAS No. 14. Parameters for these aforementioned variables are significantly positively related to AA, consistent with theory.

The Overall F-tests for Seasonal Unit Roots under Nonstationary Alternatives: Some Theoretical Results and a Monte Carlo Investigation

In many empirical studies concerning seasonal time series, it has been shown that the whole set of unit roots associated with seasonal random walks are not present. This article focuses on the overall F-tests for seasonal unit roots under some nonstationary alternatives different from the seasonal random walk. The asymptotic theory of these tests is established for these cases using a new approach based on circulant matrix concepts. The simulation results joined to this theoretic analysis showed that the overall F-tests, as well as their augmented versions, maintained high power against the nonstationary alternatives.

Investor Trading and the Post Earnings Announcement Drift

We examine whether the two distinct post-earnings-announcement drifts associated with seasonal random walk-based and analyst-based earnings surprises are attributable to the trading activities of distinct sets of investors. We predict and find that small (large) traders continue to trade in the direction of seasonal random walk-based (analyst-based) earnings surprises after earnings announcements. We also find that when small (large) traders react more thoroughly to seasonal random walk- (analyst-) based earnings surprises at the earnings announcements, the respective drift attenuates. Further evidence suggests that delayed small trades associated with random walk-based surprises are consistent with small traders’ failure to understand time-series properties of earnings, whereas delayed large trades associated with analyst-based surprises are more consistent with a longer price discovery process. We also find that the analyst-based drift has declined in recent years.

Persistence Differences of Unexpected Earnings based on Seasonal Random Walk

Persistence Differences of Unexpected Earnings based on Seasonal Random Walk

Investor Trading and the Post-Earnings-Announcement Drift

ABSTRACT: We examine whether the two distinct post-earnings-announcement drifts associated with seasonal random-walk-based and analyst-based earnings surprises are attributable to the trading activities of distinct sets of investors. We predict and find that small (large) traders continue to trade in the direction of seasonal random-walk-based (analyst-based) earnings surprises after earnings announcements. We also find that when small (large) traders react more thoroughly to seasonal random-walk- (analyst-) based earnings surprises at the earnings announcements, the respective drift attenuates. Further evidence suggests that delayed small trades associated with random-walk-based surprises are consistent with small traders’ failure to understand time-series properties of earnings, whereas delayed large trades associated with analyst-based surprises are more consistent with a longer price discovery process. We also find that the analyst-based drift has declined in recent years.

Time-series properties and predictive ability of quarterly cash flows

Abstract We provide descriptive and predictive evidence on the time-series properties and predictive ability of quarterly cash flows from operations (CFO) reported in accordance with Statement of Financial Accounting Standards (SFAS) No. 95. Previous work such as Hopwood and McKeown [Hopwood, W.S., & McKeown, J.C., (1992). Empirical evidence on the time-series properties of operating cash flows. Managerial Finance, 18, 62–78] and Lorek, Schaefer and Willinger [Lorek, K.S., Schaefer, T.F., & Willinger, G.L., (1993, January). Time-series properties and predictive ability of funds flow variables.” The Accounting Review, 68, 151–63], among others, has analyzed a proxy series (PCFO) for quarterly cash flows constructed via a relatively simplistic algorithm. We provide new evidence documenting that: (1) the time-series properties of quarterly CFO are at variance with the exclusively seasonal characterization of quarterly PCFO exhibiting both adjacent (quarter-to-quarter) and seasonal (quarter-by-quarter) relationships, (2) the Brown–Rozeff ARIMA model significantly outpredicts the random walk with drift model, seasonal random walk with drift model, and a disaggregated-accrual model, the multivariate time-series regression model (MULT) originally popularized by Lorek and Willinger [Lorek, K.S., & Willinger, G.L., (1996, January). A multivariate time-series prediction model for cash-flow data. The Accounting Review, 71, 81–101], (3) the forecast errors of larger firms are significantly smaller than the forecast errors of smaller firms, and (4) the predictive ability of the Brown–Rozeff model is robust when tested upon an expanded sample of firms (n = 745; 8940 firms/quarter predictions) obtained by eliminating the considerable data requirements of MULT.

Using the HEGY Procedure When Not All Roots Are Present

Abstract. Empirical studies have shown little evidence to support the presence of all unit roots present in the Δ4 filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo [Journal of Econometrics (1990) Vol. 44, pp. 215–238] (HEGY) procedure when the roots under the null are not all present. We exploit the vector of quarters representation and cointegration relationship between the quarters when factors (1 − L), (1 + L), (1 + L2), (1 − L2) and (1 + L + L2 + L3) are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency π/2 and two combinations of the previous cases. We show both theoretically and through a Monte Carlo analysis that the t‐ratios t and t and the F‐type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is (are) present, although this is not the case for the t‐ratio tests associated with unit roots at frequency π/2.

The contextual nature of the predictive power of statistically-based quarterly earnings models

We present new empirical evidence on the contextual nature of the predictive power of five statistically-based quarterly earnings expectation models evaluated on a holdout period spanning the twelve quarters from 2000–2002. In marked contrast to extant time-series work, the random walk with drift (RWD) model provides significantly more accurate pooled, one-step-ahead quarterly earnings predictions for a sample of high-technology firms (n = 202). In similar predictive comparisons, the Griffin-Watts (GW) ARIMA model provides significantly more accurate quarterly earnings predictions for a sample of regulated firms (n = 218). Finally, the RWD and GW ARIMA models jointly dominate the other expectation models (i.e., seasonal random walk with drift, the Brown-Rozeff (BR) and Foster (F) ARIMA models) for a default sample of firms (n = 796). We provide supplementary analyses that document the: (1) increased frequency of the number of loss quarters experienced by our sample firms in the holdout period (2000–2002) vis-a-vis the identification period (1990–1999); (2) reduced levels of earnings persistence for our sample firms relative to earnings persistence factors computed by Baginski et al. (2003) during earlier time periods (1970s–1980s); (3) relative impact on the predictive ability of the five expectation models conditioned upon the extent of analyst coverage of sample firms (i.e., no coverage, moderate coverage, and extensive coverage); and (4) sensitivity of predictive performance across subsets of regulated firms with the BR ARIMA model providing the most accurate predictions for utilities (n = 87) while the RWD model is superior for financial institutions (n = 131).