Kenneth S. Lorek, James C. McKeown, The Effect on Predictive Ability of Reducing the Number of Observations on a Time-Series Analysis of Quarterly Earnings Data, Journal of Accounting Research, Vol. 16, No. 1 (Spring, 1978), pp. 204-214

[An accurate description of the process that generates measures of funds flow (cash flow and working capital from operations) has potential importance in a variety of decision contexts. In particular, the issue of cash flow prediction has been central to standard setters. According to Statement of Financial Accounting Concepts No. 1 (FASB 1978, par. 37) "financial reporting should provide information to help investors, creditors, and others assess the amount, timing, and uncertainty of prospective net cash inflows to the related enterprise." Our first objective in this study is to provide descriptive evidence that documents the statistical patterns (e.g., seasonality, autocorrelation) of the cash flow and working capital series for a sample of firms. Although the accounting literature is replete with evidence on the time-series properties of earnings numbers, much less systematic evidence on such properties for cash flow and working capital series is presently available. Our results suggest that the time-series behavior of the cash flow series is in marked contrast to the models typically employed for accounting net income. We also provide evidence that the working capital series behaves similarly to net income. Funds flow is important in the investigation of security price effects, and the association of various measures of funds flow with security returns has been studied by Bernard and Stober (1989), Bowen et al. (1987), Schaefer and Kennelley (1986), and Wilson (1987), among others. These studies have employed cross-sectional expectation models for funds flow measures that restrict coefficients to be the same across firms. We assess the effect of such restrictions on the predictive ability of these models by comparing them with univariate time-series models that permit firm-specific estimation of coefficients. Accordingly, our second objective is to assess the accuracy of forecasts of funds flow variables generated by univariate time-series models versus those obtained from the multivariate cross-sectional models used in prior research (see, e.g., Bernard and Stober 1989; Wilson 1986, 1987). This study provides new evidence on the time-series properties of cash flow and working capital series. The empirical results indicate that the statistical patterns of the cash flow series stand in marked contrast to the well-documented characteristics of quarterly earnings data. Cash flow series are modeled parsimoniously by purely seasonal time-series models. Specifically, we provide descriptive and predictive evidence supportive of the (000)� (100) seasonal Autoregressive Integrated Moving Average (ARIMA) model as a candidate model for predicting cash flow. This model outperforms the multivariate cross-sectional models used in prior research in out-of-sample predictive ability tests. We also present evidence that working capital from operations exhibits time-series behavior virtually identical to that of accounting earnings. This results in identification of ARIMA expectation models quite similar to those popularized for quarterly earnings. Such univariate ARIMA models for working capital dominated cross-sectional regression models in tests of predictive ability.]

We present evidence on inter-firm differences in the predictive ability of quarterly earnings data for a sample of 109 New York Stock Exchange firms. The sample consisted of large, medium, and small firms after deletion of nonseasonal and volatile growth and inconsistent strata membership firms. Although the structure of the best fitting time-series models was constant across firm-size strata, we did find significant differences in the autoregressive parameters of the Foster and Brown and Rozeff ARIMA models across firm-size strata. One-step-ahead quarterly earnings forecasts were generated by a set of best fitting time-series models. A repeated measure multivariate analysis of variance design indicated that predictive ability differed on the basis of size at the .012 level. Tests also indicated that largeand medium-size firms generated one-step-ahead forecasts that were significantly more accurate than smaller firms at the .05 level. We obtained similar predictive findings on the significance of the size-effect in a supplementary analysis of the nonseasonal and volatile growth and inconsistent strata membership firms. T HE time-series properties and predictive ability of quarterly earnings data have long been topics of interest to financial accounting researchers. The focus of early work in time-series research was on the development of parsimonious models for quarterly earnings such as those popularized by Foster [1977], Griffin [1977], Watts [1975], and Brown and Rozeff [1979]. Motivation for such time-series work has been the notion that a general form seasonal model, identified from cross-sectionally derived average sample autocorrelation functions (SACFs), is sufficiently robust to represent the quarterly earnings data of firms without resorting to more complex, firm-specific alternatives. However, more recent work by Lorek and Bathke [1984] provides evidence that the quarterly earnings of certain firms behave in a nonseasonal manner systematically different from that suggested by the parsimonious models.1 This raises the issue of whether systematic differ' All three parsimonious models contain either seasonal differencing and/or seasonal moving average

[We present evidence on inter-firm differences in the predictive ability of quarterly earnings data for a sample of 109 New York Stock Exchange firms. The sample consisted of large, medium, and small firms after deletion of nonseasonal and volatile growth and inconsistent strata membership firms. Although the structure of the best fitting time-series models was constant across firm-size strata, we did find significant differences in the autoregressive parameters of the Foster and Brown and Rozeff ARIMA models across firm-size strata. One-step-ahead quarterly earnings forecasts were generated by a set of best fitting time-series models. A repeated measure multivariate analysis of variance design indicated that predictive ability differed on the basis of size at the.012 level. Tests also indicated that large-and medium-size firms generated one-step-ahead forecasts that were significantly more accurate than smaller firms at the.05 level. We obtained similar predictive findings on the significance of the size-effect in a supplementary analysis of the nonseasonal and volatile growth and inconsistent strata membership firms.]

This article reports the results of an empirical study which has bearing upon issues of the accuracy of management forecasts of income in particular and the time series properties of earnings data. From the standpoint of whether corporate forecasts of earnings should be disclosed, the question of accuracy is relevant. This article utilizes the Box-Jenkins methodology in the determination of the most appropriate time series model for each firm in the sample. The proposition that management forecasts of income should prove fairly accurate is not supported by the results of this study. In cases in which management forecasts proved reasonably accurate, overall they were not more so than those generated from the time series models. It remains possible that the management forecasts may contain additional information regarding risk or return. For example, market participants may use management forecasts and time series analysis. With respect to the time series properties of quarterly earnings, the results clearly demonstrate the significance of seasonality in quarterly earnings.

ABSTRACT: We present evidence on inter-firm differences in the predictive ability of quarterly earnings data for a sample of 109 New York Stock Exchange firms. The sample consisted of large, medium, and small firms after deletion of nonseasonal and volatile growth and inconsistent strata membership firms. Although the structure of the best fitting time-series models was constant across firm-size strata, we did find significant differences in the autoregressive parameters of the Foster and Brown and Rozeff ARIMA models across firm-size strata. One-step-ahead quarterly earnings forecasts were generated by a set of best fitting time-series models. A repeated measure multivariate analysis of variance design indicated that predictive ability differed on the basis of size at the .012 level. Tests also indicated that large-and medium-size firms generated one-step-ahead forecasts that were significantly more accurate than smaller firms at the .05 level. We obtained similar predictive findings on the significance of the size-effect in a supplementary analysis of the nonseasonal and volatile growth and inconsistent strata membership firms.

Accounting researchers (and potentially others) generally select rather simple, lower-order, time-series models to develop proxies for earnings persistence. However, measures of persistence produced by such models are not related to characteristics of the firm's economic environment that are expected to influence earnings persistence. Using a sample of 162 calendar year-end New York Stock Exchange firms, we document the cross-sectional relations between a set of relatively constant, firm-specific, economic characteristics that are theoretical determinants of persistence and measures of earnings persistence derived from both lower-order and higher-order Autoregressive, Integrated, Moving-Average (ARIMA) models. When lower-order ARIMA models are used to generate measures of earnings persistence, the cross-sectional regression models measuring the association between persistence and economic determinants of persistence yield very low adjusted R2s. In sharp contrast, when differenced, higher-order ARIMA models are used to measure earnings persistence, adjusted R2s are in the 10–12 percent range. Moreover, independent variables such as capital intensity, barriers-to-entry, and product-type are all significant in the directions suggested by economic theory. Our results are consistent with Lipe and Kormendi (1994) who argue that higher-order ARIMA models do a better job of capturing the valuerelevance of current period earnings than lower-order models.