On the forecasting of high-frequency financial time series based on ARIMA model improved by deep learning

Through empirical research, it is found that the traditional autoregressive integrated moving average (ARIMA) model has a large deviation for the forecasting of high-frequency financial time series. With the improvement in storage capacity and computing power of high-frequency financial time series, this paper combines the traditional ARIMA model with the deep learning model to forecast high-frequency financial time series. It not only preserves the theoretical basis of the traditional model and characterizes the linear relationship, but also can characterize the nonlinear relationship of the error term according to the deep learning model. The empirical study of Monte Carlo numerical simulation and CSI 300 index in China show that, compared with ARIMA, support vector machine (SVM), long short-term memory (LSTM) and ARIMA-SVM models, the improved ARIMA model based on LSTM not only improves the forecasting accuracy of the single ARIMA model in both fitting and forecasting, but also reduces the computational complexity of only a single deep learning model. The improved ARIMA model based on deep learning not only enriches the models for the forecasting of time series, but also provides effective tools for high-frequency strategy design to reduce the investment risks of stock index.     

Analysis and forecasting of income statement account balances the dynamic interdependency and ARIMA approaches

This paper develops a dynamic simultaneous-equations model for analyzing and forecasting the account balances in the income statement of a firm. In the model, the income statement accounts play the role of the dependent variables that are jointly determined and explained by three types of exogenous variables: non-controllable, performance, and controllable. The model is estimated by the three-stage least-squares method using annual series of data for six firms during the period from 1936 or 1950 to 1981. The immediate, delayed, and cumulated impacts of an exogenous shock on the income accounts are analyzed and the implications for managerial decisions and strategies discussed. To run as a standard of comparison for the dynamic interdependency model, the Box-Jenkins approach is also used to develop an autoregressive integrated moving average (ARIMA) model for each of the accounts. Assessing the forecasting performance of the dynamic model against a naive model and the ARIMA and Elliott-Uphoff models for the 1982-4 period beyond the estimation period, we conclude that the dynamic model is a better representation of income statement accounts of the firm and increases forecasting accuracy.     

Forecasting time series with increasing seasonal variation

Four options for modeling and forecasting time series data containing increasing seasonal variation are discussed, including data transformations, double seasonal difference models and two kinds of transfer function-type ARIMA models employing seasonal dummy variables. An explanation is given for the typical ARIMA model identification analysis failing to identify double seasonal difference models for this kind of data. A logical process of selecting one option for a particular case is outlined, focusing on issues of linear versus non-linear increasing seasonal variation, and the level of stochastic versus deterministic behavior in a time series. Example models for the various options are presented for six time series, with point forecast and interval forecast comparisons. Interval forecasts from data-transformation models are found to generally be too wide and sometimes illogical in the dependence of their width on the point forecast level. Suspicion that maximum likelihood estimation of ARIMA models leads to excessive indications of unit roots in seasonal moving-average operators is reported.     

A New‐Keynesian DSGE model for forecasting the South African economy

This paper develops a New‐Keynesian Dynamic Stochastic General Equilibrium (NKDSGE) model for forecasting the growth rate of output, inflation, and the nominal short‐term interest rate (91 days Treasury Bill rate) for the South African economy. The model is estimated via maximum likelihood technique for quarterly data over the period of 1970:1–2000:4. Based on a recursive estimation using the Kalman filter algorithm, out‐of‐sample forecasts from the NKDSGE model are compared with forecasts generated from the classical and Bayesian variants of vector autoregression (VAR) models for the period 2001:1–2006:4. The results indicate that in terms of out‐of‐sample forecasting, the NKDSGE model outperforms both the classical and Bayesian VARs for inflation, but not for output growth and nominal short‐term interest rate. However, differences in RMSEs are not significant across the models. Copyright © 2008 John Wiley & Sons, Ltd.     

Sales forecasting using multi-equation transfer function models

The purpose of this study is first, to demonstrate how multivariate forecasting models can be effectively used to generate high performance forecasts for typical business applications. Second, this study compares the forecasts generated by a simultaneous transfer function model (STF) model and a white noise regression model with that of a univariate ARIMA model. The accuracy of these forecasting models is judged using their residual variances and forecasting errors in a post-sample period. It is found that ignoring the residual serial correlation can greatly degrade the forecasting performance of a multi-variable model, and in some situations, cause a multi-variable model to perform inferior to a univariate ARIMA model. This paper also demonstrates how a forecaster can use an STF model to compute both the multi-step ahead forecasts and their variances easily.     

On a family of finite moving‐average trend filters for the ends of series

A family of finite end filters is constructed using a minimum revisions criterion and based on a local dynamic model operating within the span of a given finite central filter. These end filters are equivalent to evaluating the central filter with unavailable future observations replaced by constrained optimal linear predictions. Two prediction methods are considered: best linear unbiased prediction and best linear biased prediction where the bias is time invariant. The properties of these end filters are determined. In particular, they are compared to X‐11 end filters and to the case where the central filter is evaluated with unavailable future observations predicted by global ARIMA models as in X‐11‐ARIMA or X‐12‐ARIMA. Copyright © 2002 John Wiley & Sons, Ltd.     

Sales revenues: Time-series properties and predictions

This paper compares the predictive ability of ARIMA models in forecasting sales revenue. Comparisons were made at both industry and firm levels. With respect to the form of the ARIMA model, a parsimonious model of the form (0, 1, 1) (0, 1, 1) was identified most frequently for firms and industries. This model was identified previously by Griffin and Watts for the earnings series, and by Moriarty and Adams for the sales series. As a parsimonious model, its predictive accuracy was quite good. However, predictive accuracy was also found to be a function of the industry. Out of the eleven industry classifications, ‘metals’ had the lowest predictive accuracy using both firmspecific and industry-specific ARIMA models.     

Performance of GARCH models in forecasting stock market volatility

This paper studies the performance of GARCH model and its modifications, using the rate of returns from the daily stock market indices of the Kuala Lumpur Stock Exchange (KLSE) including Composite Index, Tins Index, Plantations Index, Properties Index, and Finance Index. The models are stationary GARCH, unconstrained GARCH, non‐negative GARCH, GARCH‐M, exponential GARCH and integrated GARCH. The parameters of these models and variance processes are estimated jointly using the maximum likelihood method. The performance of the within‐sample estimation is diagnosed using several goodness‐of‐fit statistics. We observed that, among the models, even though exponential GARCH is not the best model in the goodness‐of‐fit statistics, it performs best in describing the often‐observed skewness in stock market indices and in out‐of‐sample (one‐step‐ahead) forecasting. The integrated GARCH, on the other hand, is the poorest model in both respects. Copyright © 1999 John Wiley & Sons, Ltd.     

Weights and robustness of model-based seasonal adjustment

Model-based seasonal adjustment implicitly defines a set of weights at the ends of series as well as in the middle. Until now, with the exception of very simple models, the weights have been obtained numerically. In this paper we give the analytical expressions for the weights for both the structural and the ARIMA framework for a model which contains trend, seasonal and irregular component. In the final part of the paper we address the question of robustness of model-based seasonal adjustment. We analyse practically, using real time series, and theoretically, through the analysis of the shape of the weights, how the fitting of different specifications for the non-seasonal part affects the extraction of the seasonal component. © 1998 John Wiley & Sons, Ltd.     

Forecasting the federal budget with time-series models

The stochastic properties of conventionally denned federal expenditures and revenues are examined, and cointegration is found. Alternative time-series models-univariate ARIMA models, vector autoregressions in levels and differences, and an error correction model-are specified and estimated using quarterly data from 1955:1 through 1979:4. Updated forecasts for up to three years beyond the sample period are evaluated against actual expenditures, revenues and the deficit. The vector autoregression in levels shows evidence of nonstationarity, which leads to strong biases in the forecasts. The remaining models produce forecasts that are satisfactory by the mean squared error criterion, and the magnitudes of biases at the longer horizons are significantly smaller than those of the official forecasts.     

Parameter Space Restrictions in State Space Models

The state space model is widely used to handle time series data driven by related latent processes in many fields. In this article, we suggest a framework to examine the relationship between state space models and autoregressive integrated moving average (ARIMA) models by examining the existence and positive‐definiteness conditions implied by auto‐covariance structures. This study covers broad types of state space models frequently used in previous studies. We also suggest a simple statistical test to check whether a certain state space model is appropriate for the specific data. For illustration, we apply the suggested procedure in the analysis of the United States real gross domestic product data. Copyright © 2011 John Wiley & Sons, Ltd.     

Forecasting with balanced state space representations of multivariate distributed lag models

A procedure for estimating state space models for multivariate distributed lag processes is described. It involves singular value decomposition techniques and yields an internally balanced state space representation which has attractive properties. Following the specifications of a forecasting competition, the approach is applied to generate ex-post forecasts for US real GNP growth rates. The forecasts of the estimated state space model are compared to those of twelve econometric models and an ARIMA model.     

The Effect of Estimating Parameters on Long‐Term Forecasts for Cointegrated Systems

This paper concerns Long‐term forecasts for cointegrated processes. First, it considers the case where the parameters of the model are known. The paper analytically shows that neither cointegration nor integration constraint matters in Long‐term forecasts. It is an alternative implication of Long‐term forecasts for cointegrated processes, extending the results of previous influential studies. The appropriate Mote Carlo experiment supports our analytical result. Secondly, and more importantly, it considers the case where the parameters of the model are estimated. The paper shows that accuracy of the estimation of the drift term is crucial in Long‐term forecasts. Namely, the relative accuracy of various Long‐term forecasts depends upon the relative magnitude of variances of estimators of the drift term. It further experimentally shows that in finite samples the univariate ARIMA forecast, whose drift term is estimated by the simple time average of differenced data, is better than the cointegrated system forecast, whose parameters are estimated by the well‐known Johansen's ML method. Based upon finite sample experiments, it recommends the univariate ARIMA forecast rather than the conventional cointegrated system forecast in finite samples for its practical usefulness and robustness against model misspecifications. Copyright © 2011 John Wiley & Sons, Ltd.     

Linear constraints,robust-weighting and efficient composite modeling

Recent studies have shown that composite forecasting produces superior forecasts when compared to individual forecasts. This paper extends the existing literature by employing linear constraints and robust regression techniques in composite model building. Security analysts forecasts may be improved when combined with time series forecasts for a diversified sample of 261 firms with a 1980-1982 post-sample estimation period. The mean square error of analyst forecasts may be reduced by combining analyst and univariate time series model forecasts in constrained and unconstrained ordinary least squares regression models. These reductions are very interesting when one finds that the univariate time series model forecasts do not substantially deviate from those produced by ARIMA (0,1,1) processes. Moreover, security analysts' forecast errors may be significantly reduced when constrained and unconstrained robust regression analyses are employed.     

Seasonal variations in fat body metabolism of the green frog Rana esculenta (L.).

Rana esculenta (L.), kept under natural conditions, show almost constant body weights in the annual cycle. Fat body weight, however, has a distinct maximum in October decreasing continuously to a May minimum which is also evident in the fat body index. The triglyceride and protein contents show the same course. Suprisingly high amounts of glycogen are found, which reach a maximum in August.     

A comparative arima analysis of the 111 series of the makridakis competition

The 111 series of the Makridakis competition are used to address a number of questions pertaining to use of the Box–Jenkins technique. The ARIMA models developed are compared to the ARIMA models developed independently by Andersen for the Makridakis competition. The time required to perform the analysis for each series is discussed in terms of model complexity. Forecast accuracy, measured as the MAPE for the one step ahead forecast, is discussed for different series lengths.     

Forecasting the recent behavior of US business fixed investment spending: an analysis of competing models

We evaluate forecasting models of US business fixed investment spending growth over the recent 1995:1–2004:2 out‐of‐sample period. The forecasting models are based on the conventional Accelerator, Neoclassical, Average Q, and Cash‐Flow models of investment spending, as well as real stock prices and excess stock return predictors. The real stock price model typically generates the most accurate forecasts, and forecast‐encompassing tests indicate that this model contains most of the information useful for forecasting investment spending growth relative to the other models at longer horizons. In a robustness check, we also evaluate the forecasting performance of the models over two alternative out‐of‐sample periods: 1975:1–1984:4 and 1985:1–1994:4. A number of different models produce the most accurate forecasts over these alternative out‐of‐sample periods, indicating that while the real stock price model appears particularly useful for forecasting the recent behavior of investment spending growth, it may not continue to perform well in future periods. Copyright © 2007 John Wiley & Sons, Ltd.     

Operational filtering of traffic data

An operational filter of traffic state variables is presented for use in designing computer-aided traffic surveillance and control systems. A total of 166 data sets from three traffic surveillance systems were used in the filter development. All the data sets were best represented by an ARIMA (0,1,3) filter. This filter has the following advantages: (1) it yields minimum mean-square-error forecasts if stationarity of the observations can be obtained; (2) it provides much better results than the existing ad hoc filters; (3) it is computationally tractable; and (4) it requires modest computer storage of data. Suggestions and implications for the use of this filter are given.     

Seasonal variations in fat body metabolism of the green frogRana esculenta (L.)

Summary Rana esculenta (L.), kept under natural conditions, show almost constant body weights in the annual cycle. Fat body weight, however, has a distinct maximum in October decreasing continuously to a May minimum which is also evident in the fat body index. The triglyceride and protein contents show the same course. Surprizingly high amounts of glycogen are found, which reach a maximum in August.     

ARIMA models of the price level: An assessment of the multilevel adaptive learning process in the USA

This paper estimates the ARIMA processes for the observed and expected price level corresponding to the three-level adaptive expectations model proposed by Jacobs and Jones (1980). These univariate processes are then compared with the best-fit ARIMA model. The results indicate that the best-fit model for the observed price level is a restricted version of the two-level adaptive learning process specified in terms of prices, suggesting a simple adaptive rule in the inflation rate. A comparison of the time-series forecasts from the best-fit model with the mean responses to the ASA-NBER survey shows no significant difference in their accuracy. The time-series forecasts are, however, conditionally efficient. The best-fit ARIMA model for expected prices measured by the ASA-NBER consensus forecasts does not correspond to any version of the Jacobs and Jones model.