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Seasonal Adjustment as a Practical Problem.

作为实践问题的季节调整

Seasonal adjustment as a practical problem. Prolegomena to actual seasonal adjustment. Mechanical seasonal adjustment methods. ARIMA models and seasonal adjustment. Structural time series models and seasonal adjustment. The adding up problem and seasonally adjusted monetary analysis. Causal methods of seasonal adjustment. Concluding observations. Annex. References. Indexes.

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On Concurrent Seasonal Adjustment

同期季节调整

Concurrent seasonal adjustment uses all information up to and including the current month's figure and thus should provide more accurate estimates of final seasonally adjusted data than the prevalent official method where the current month's component is forecasted from data through the preceding December. This article evaluates the expected gain from employing concurrent seasonal adjustment, including the case in which the data contain both nonseasonal and seasonal…

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On Concurrent Seasonal Adjustment

同期季节调整

Concurrent seasonal adjustment uses all information up to and including the current month's figure and thus should provide more accurate estimates of final seasonally adjusted data than the prevalent official method where the current month's component is forecasted from data through the preceding December. This article evaluates the expected gain from employing concurrent seasonal adjustment, including the case in which the data contain both nonseasonal and seasonal…

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Estimating Trend and Growth Rates in Seasonal Time Series

季节时间序列的趋势与增长率估计

We consider the problem of trend estimation from an ARIMA-model-based perspective. Given that the time series of interest is well represented by a multiplicative seasonal ARIMA model (Box and Jenkins 1970), a method is presented for estimating the trend of this series as a component of the model's forecast function. This method is applied to the “airline model,” a commonly occurring model form for economic and social time series. For those numerous series that are rendered…

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Estimating Trend and Growth Rates in Seasonal Time Series

季节性时间序列的趋势与增长率估计

We consider the problem of trend estimation from an ARIMA-model-based perspective. Given that the time series of interest is well represented by a multiplicative seasonal ARIMA model (Box and Jenkins 1970), a method is presented for estimating the trend of this series as a component of the model's forecast function. This method is applied to the “airline model,” a commonly occurring model form for economic and social time series. For those numerous series that are rendered…

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Seasonal Adjustment of the Weekly Monetary Aggregates: A Model-Based Approach

周度货币总量的季节调整:基于模型的方法

A procedure is developed for seasonally adjusting weekly time series, based on a composite of regression and time series models. The procedure is applied to some weekly U.S. money supply series currently seasonally adjusted by the Federal Reserve.

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Seasonal Adjustment of the Monetary Aggregates: Summary of the Federal Reserve's Committee Report

货币总量的季节调整:美联储委员会报告概要

The Committee of Experts on Seasonal Adjustment Techniques was formed by the Federal Reserve Board to examine and make recommendations concerning the Board's procedures for seasonally adjusting the money supply and related series. This article summarizes the report of that committee.

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R 2 Measures for Time Series

时间序列的决定系数度量

With time series data, the conventional regression R 2 is a nebulous concept, as the explained variation consists in part of variation that can be attributed merely to past values of the dependent variable. Thus R 2 is extremely sensitive to prefiltering operations such as first differencing. This article develops and illustrates an alternative R 2 concept, which eliminates this ambiguity by measuring the explanatory power of a time series-regression model relative to that…

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Signal Extraction Error in Nonstationary Time Series

非平稳时间序列中的信号提取误差

It is supposed that an observable time series $\{x_t\}$ is representable as the sum of a "signal" $s_t$ and a "noise" $n_t$, and that it is desired to extract the signal $s_t$, i.e., to obtain an estimate $\hat{s}_t$ of $s_t$. Corresponding to any such estimate is a signal extraction error, $\delta_t = s_t - \hat{s}_t$, which for nondeterministic stochastic processes possesses a nonzero mean square. For the class of homogeneously nonstationary processes, characterizations of…

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Relationships—and the Lack Thereof—Between Economic Time Series, with Special Reference to Money and Interest Rates

经济时间序列的联系及其缺失:货币与利率

Extensions of time-series modeling procedures of Box and Jenkins [5] reveal that numerous economic variables which are generally regarded as being strongly interrelated may with equal validity, based on recent empirical evidence, be regarded as independent or only weakly related. Differences between these results and the bulk of econometric literature are attributed to the failure of the latter to satisfactorily account for autocorrelation. Due to limitations in the data, it…

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Residual Correlations and Diagnostic Checking in Dynamic-Disturbance Time Series Models

动态扰动时间序列模型的残差相关与诊断检查

In examining adequacy of fit of a statistical model the stochastic properties of the residuals are often studied. In particular, for an important class of time series models involving an exogenous or input variable and correlated errors or disturbances, Box and Jenkins [1] recommend an examination of the autocorrelations of the residuals and the cross correlations between the residuals and the independent variable. It is shown in this article that the residual auto- and…

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Least Squares Estimation in Dynamic-Disturbance Time Series Models

动态扰动时间序列模型中的最小二乘估计

Recent results of the author concerning large-sample properties of the nonlinear least squares estimates of the parameters, in a regression model in which the disturbances follow a stationary mixed autoregressive-moving average time series, are extended to models in which lagged values of the dependent and independent variables occur.

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Least Squares Estimation in the Regression Model with Autoregressive-Moving Average Errors

具有自回归移动平均误差的回归模型的最小二乘估计

To treat the problem of correlated errors in regression, a model in which the errors follow a stationary autoregressive-moving average time series is suggested. Simultaneous least squares estimation of the regression and the time series parameters is discussed, and it is shown that asymptotically the estimates obtained in this manner possess normal distributions, whether or not the errors themselves are normally distributed. The estimates of the regression parameters are…

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Distribution of Residual Autocorrelations in the Regression Model with Autoregressive–Moving Average Errors

自回归移动平均误差回归模型中残差自相关的分布

Summary In examining the adequacy of a statistical model an analysis of the residuals is often carried out; and for models involving a time series structure the serial correlations of the residuals are natural statistics to consider. In this paper it is shown that asymptotically the first s sample autocorrelations of the residuals, calculated from a least-squares fit of a regression model in which the errors follow a stationary autoregressive–moving average time series,…

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Least squares estimation in the regression model with autoregressive-moving average errors

自回归移动平均误差回归模型的最小二乘估计

To treat the problem of correlated errors in regression, a model in which the errors follow a stationary autoregressive-moving average time series is suggested. Simultaneous least squares estimation of the regression and the time series parameters is discussed, and it is shown that asymptotically the estimates obtained in this manner possess normal distributions, whether or not the errors themselves are normally distributed. The estimates of the regression parameters are…

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Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models

ARIMA 时间序列模型中残差自相关的分布

Many statistical models, and in particular autoregressive—moving average time series models, can be regarded as means of transforming the data to white noise, that is, to an uncorrected sequence of errors. If the parameters are known exactly, this random sequence can be computed directly from the observations; when this calculation is made with estimates substituted for the true parameter values, the resulting sequence is referred to as the “residuals,” which can be regarded…

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