Geometrical Interpretation of the Mean and the Constant in a Box-Jenkins Time Series Model

Certain manuals and computer programs mistakenly identify the mean with the constant in Box-Jenkins time series models. In this paper, it will be shown that (a) the mean and the constant have different values in autoregressive models, and (b) they have an algebraic and graphical relationship.     

Does the Phillips curve help to forecast euro area inflation?

We find that it does, but choosing the right specification is not trivial. Based on an extensive forecast evaluation we document notable forecast instabilities for most simple Phillips curves. Euro area inflation was particularly hard to forecast in the run-up to the Economic and Monetary Union and after the sovereign debt crisis, when the trends—and, for the latter period, also the amount of slack—were harder to pin down. Yet, some specifications outperform a univariate benchmark and point to the following lessons: (i) the key type of time variation to consider is an inflation trend; (ii) a simple filter-based output gap works well, but after the Great Recession it is outperformed by endogenously estimated slack or by “institutional” estimates; (iii) external variables do not bring forecast gains; (iv) newer-generation Phillips curve models with several time-varying features are a promising avenue for forecasting; and (v) averaging over a wide range of modelling choices helps.     

湖南省地区生产总值ARMA分析

运用计量经济学原理对湖南省1952年以来地区生产总值进行动态分析,建立了ARMA模型,并利用历史数据论证模型的正确性,研究地区生产总值变化趋势和特征,给出了地区生产总值的预测方法,为经济决策提供依据。     

Would the Bundesbank have prevented the Great Inflation in the United States?

Policy counterfactuals based on estimated structural VARs routinely suggest that bringing Alan Greenspan back in the 1970s United States would not have prevented the Great Inflation. We show that a standard policy counterfactual suggests that the Bundesbank—which is near-universally credited for sparing West Germany the Great Inflation—would also not have been able to prevent the Great Inflation in the United States.The implausibility of this result sounds a cautionary note on taking the outcome of SVAR-based policy counterfactuals at face value, and raises questions on the reliability of such exercises.     

Evaluating factor forecasts for the UK: The role of asset prices

This paper applies a large data set, consisting of 167 monthly time series for the UK, both economic and financial, to simulate out-of-sample predictions of industrial production, inflation, 3-month Treasury Bills, and other variables. Fifteen dynamic factor models that allow forecasting based on large panels of time series are considered. The performances of these factor models are then compared to the following competing models: a simple univariate autoregressive, a vector autoregressive, a leading indicator, and a Phillips curve models. The results show that the best dynamic factor models outperform the competing models in forecasting at 6-, 12-, and 24-month horizons. Thus, the financial markets may have predictive power for the economic activity. This can be a useful tool for central banks and financial institutions, which may use the factor models to construct leading indicators of the economic conditions. In addition, researchers can see a strategic application of factor models.     

Trends, lead times and forecasting

The innovations representation for a local linear trend can adapt to long run secular and short term transitory effects in the data. This is illustrated by the theoretical power spectrum for the model which may possess considerable power at frequencies that might be associated with cycles of several years' duration. Whilst advantageous for short term forecasting, the model may be of less use when interest is in the underlying long run trend in the data. In this paper we propose a generalisation of the innovations representation for a local linear trend that is appropriate for representing short, medium and long run trends in the data.     

Graphical interaction models for multivariate time series1

In this paper we extend the concept of graphical models for multivariate data to multivariate time series. We define a partial correlation graph for time series and use the partial spectral coherence between two components given the remaining components to identify the edges of the graph. As an example we consider multivariate autoregressive processes. The method is applied to air pollution data. Received: June 1999     

Short Time Series Analysis: C Statistic vs Edgington Model

Young's C statistic (1941) makes it possible to compare the randomization of a set of sequentially organized data and constitutes an alternative of appropriate analysis in short time series designs. On the other hand, models based on the randomization of stimuli are also very important within the behavioral content applied. For this reason, a comparison is established between the C statistic and the Edgington model. The data analyzed in the comparative study have been obtained from graphs in studies published in behavioral journals. According to the results obtained, it is concluded that the Edgington model in experimental designs AB involves many measurements while the C statistic requires fewer observations to reach the conventional significance level.     

Bayesian Comparison of ARIMA and Stationary ARMA Models

Time series analysts have long been concerned with distinguishing stationary generating processes from processes for which differencing is required to induce stationarity. In practical applications, this issue is addressed almost invariably through formal hypothesis testing. In this paper, we explore some aspects of the Bayesian approach to the problem, leading to the calculation of posterior odds ratios. Interesting features arise in the simplest possible variant of the problem, where a choice has to be made between a random walk and a stationary first order autoregressive model. We discuss in detail the analysis of this case, and also indicate how our approach extends to the more general comparison of an ARIMA model with a stationary competitor.     

Moment-based estimation of smooth transition regression models with endogenous variables

Nonlinear regression models have been widely used in practice for a variety of time series and cross-section datasets. For purposes of analyzing univariate and multivariate time series data, in particular, smooth transition regression (STR) models have been shown to be very useful for representing and capturing asymmetric behavior. Most STR models have been applied to univariate processes, and have made a variety of assumptions, including stationary or cointegrated processes, uncorrelated, homoskedastic or conditionally heteroskedastic errors, and weakly exogenous regressors. Under the assumption of exogeneity, the standard method of estimation is nonlinear least squares. The primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss moment-based methods for estimating STR models. The paper analyzes the properties of the STR model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity, developing an estimation procedure and a misspecification test for the STR model, presenting the results of Monte Carlo simulations to show the usefulness of the model and estimation method, and providing an empirical application for inflation rate targeting in Brazil. We show that STR models with endogenous variables can be specified and estimated by a straightforward application of existing results in the literature.     

Relationship between the Mean and the Constant in a Box–Jenkins Time Series Model

In some publications the mean is identified with the constant of a Box–Jenkins time series model. In this paper the relation between both terms is demonstrated. Furthermore, by means of an example, the errors which may be made if one does not use each term adequately are shown.     

Seasonal exponential smoothing with damped trends : An application for production planning

This paper reviews a spreadsheet-based forecasting approach which a process industry manufacturer developed and implemented to link annual corporate forecasts with its manufacturing/distribution operations. First, we consider how this forecasting system supports overall production planning and why it must be compatible with corporate forecasts. We then review the results of substantial testing of variations on the Winters three-parameter exponential smoothing model on 28 actual product family time series. In particular, we evaluate whether the use of damping parameters improves forecast accuracy. The paper concludes that a Winters four-parameter model (i.e. the standard Winters three-parameter model augmented by a fourth parameter to damp the trend) provides the most accurate forecasts of the models evaluated. Our application confirms the fact that there are situations where the use of damped trend parameters in short-run exponential smoothing based forecasting models is beneficial.     

Prediction intervals in conditionally heteroscedastic time series with stochastic components

Differencing is a very popular stationary transformation for series with stochastic trends. Moreover, when the differenced series is heteroscedastic, authors commonly model it using an ARMA-GARCH model. The corresponding ARIMA-GARCH model is then used to forecast future values of the original series. However, the heteroscedasticity observed in the stationary transformation should be generated by the transitory and/or the long-run component of the original data. In the former case, the shocks to the variance are transitory and the prediction intervals should converge to homoscedastic intervals with the prediction horizon. We show that, in this case, the prediction intervals constructed from the ARIMA-GARCH models could be inadequate because they never converge to homoscedastic intervals. All of the results are illustrated using simulated and real time series with stochastic levels.