Stationary Time Series Data Research Articles

A smoothed bootstrap test for independence based on mutual information

A test for independence of multivariate time series based on the mutual information measure is proposed. First of all, a test for independence between two variables based on i.i.d. (time-independent) data is constructed and is then extended to incorporate higher dimensions and strictly stationary time series data. The smoothed bootstrap method is used to estimate the null distribution of mutual information. The experimental results reveal that the proposed smoothed bootstrap test performs better than the existing tests and can achieve high powers even for moderate dependence structures. Finally, the proposed test is applied to assess the actual independence of components obtained from independent component analysis (ICA).

평활된 주기도를 이용한 강수량자료의 군집화

It is well known that spectral density function determines auto-covariance function of stationary time-series data and smoothed periodogram is a consistent estimator of spectral density function. Recently, Kim and Park (2007) showed that smoothed- periodogram based distances performs very well for the classification. In this paper, we introduce classification methods with smoothed periodogram and apply the approaches to the monthly precipitation measurements obtained from January, 1987 through December, 2007 at 22 locations in South Korea.

The Growth‐Finance Relationship: The Case of Jordan 1970‐2002

The present study investigates the dynamic effects of domestic credit measured by claims on non financial public enterprises and claims on private sector on the real GDP in Jordan for the period 1970‐2002. The stationarity properties and the order of integration of the data employed were empirically examined using the Augmented Dickey‐Fuller test. The cointegration test proposed by Johansen was also employed to test for the existence of longrun relationship among the non stationary time series data. The result of the cointegration test suggests that there exists a cointegrating relationship between real GDP and claims on private sector. The short‐run and long‐run relationships between real GDP and claims on private sector were examined using the VEC technique. In the short run, real GDP turns out to have an impact which is statistically significant on the claims on private sector, while in the long run, the claims on private sector turn out to affect real GDP at the 1% significance level.

STOCHASTIC SUBSPACE IDENTIFICATION GUARANTEEING STABILITY AND MINIMUM PHASE

This paper presents a stochastic subspace identification algorithm to compute stable, minimum phase models from a stationary time-series data. The algorithm is based on spectral factorization techniques and a stochastic subspace identification method via a block LQ decomposition (Tanaka and Katayama, 2003c). Two Riccati equations are solved to ensure both stability and minimum phase property of resulting Markov models.

Model identification of ARIMA family using genetic algorithms

ARIMA is a popular method to analyze stationary univariate time series data. There are usually three main stages to build an ARIMA model, including model identification, model estimation and model checking, of which model identification is the most crucial stage in building ARIMA models. However there is no method suitable for both ARIMA and SARIMA that can overcome the problem of local optima. In this paper, we provide a genetic algorithms (GA) based model identification to overcome the problem of local optima, which is suitable for any ARIMA model. Three examples of times series data sets are used for testing the effectiveness of GA, together with a real case of DRAM price forecasting to illustrate an application in the semiconductor industry. The results show that the GA-based model identification method can present better solutions, and is suitable for any ARIMA models.

Modeling of time series arrays by multistep prediction or likelihood methods

An estimation theory is provided for the fitting of possibly incorrect, invertible, short-memory models to (short- or long-memory) time series or time series arrays by multistep prediction error minimization or Gaussian likelihood maximization. By array, we mean data y t ( T ),1⩽ t ⩽ T , that depend on the number of observations T , such as regression or other estimated-model residuals, or the outputs of time varying filters, for example seasonal adjustments. Our theory only requires the modeled array to have basic properties: for a.s. [i.p.] convergence of parameter estimates, the array's sample lagged second moments must converge a.s. [i.p.], and its end values y 1+ j ( T ) and y T − j ( T ) must be of order less than T 1/2 . Or an appropriately differenced version of the observed array must have these properties. In Findley et al. (Ann. Statist. 29 (2001) 815), broad classes of arrays were shown to have these properties. Even for the special case of autoregressive moving average models fit to stationary Gaussian time series data, our result on the convergence of parameter estimates minimizing p -step-ahead prediction error sums of squares is new.

Bootstrapping stationary sequences by the Nadaraya-Watson regression estimator

We propose a new bootstrap method for stationary time series data which uses the Nadaraya-Watson kernel regression estimator. We call this method N-W bootstrap. The N-W bootstrap consists of estimating the conditional autoregressive mean function by the Nadaraya-Watson estimator and bootstrapping the resulting residuals. Indeed we obtain a bootstrapped copy by regenerating a stationary time series data from the Nadaraya-Watson regression estimates and their bootstrapped residuals. A Monte Carlo simulation study is conducted to compare our method to the block bootstrap method (Ku¨nsch, 1989 or Liu and Singh, 1992) in various time series models, which shows the performance of the N-W bootstrap is better or at least comparable to the block bootstrap. Some practical usefulness of the N-W bootstrap is also discussed.

Time series forecasts of international travel demand for Australia

This paper analyses stationary and non-stationary international tourism time series data by formally testing for the presence of unit roots and seasonal unit roots prior to estimation, model selection and forecasting. Various Box–Jenkins Autoregressive Integrated Moving Average (ARIMA) models are estimated over the period 1975(1)–1989(4) for tourist arrivals to Australia from Hong Kong, Malaysia and Singapore. The mean absolute percentage error and root mean squared error (RMSE) are used as measures of forecast accuracy. As the best fitting ARIMA model is found to have the lowest RMSE, this model is used to obtain post-sample forecasts. Tourist arrivals data for 1990(1)–1996(4) are compared with the forecast performance of the ARIMA model for each origin market. The fitted ARIMA model forecasts tourist arrivals from Singapore for the period 1990(1)–1996(4) very well. Although the ARIMA model outperforms the seasonal ARIMA models for Hong Kong and Malaysia, the forecasts of tourist arrivals are not as accurate as in the case of Singapore.

Tests for Asymmetry in Possibly Nonstationary Time Series Data

Tests for asymmetric adjustment in possibly nonstationary, nearly nonstationary, or stationary time series data are developed. The asymmetry is modeled by the momentum threshold autoregressive model of Enders and Granger and an extension of it. The tests are t-type tests and Wald tests based on instrumental-variable estimators and are asymptotically normal or chi-squared regardless of stationarity/nonstationarity of data-generating processes. This is in contrast to the fact that the ttests and the Wald tests based on the ordinary least squares estimator (OLSE) are asymptotically normal and chisquared, respectively, only under stationarity and are thus statistically invalid under nonstationarity. A Monte Carlo simulation shows that the proposed tests have stable sizes. Powers of the proposed tests against stationary alternatives are comparable to those of the OLSE-based tests. The Monte Carlo study also shows that the new estimators are less biased than the OLSE when data-generating processes are random walks. The proposed tests are applied to a monthly U.K. interest-rate dataset to find evidences for asymmetry in directions of adjustments as well as in amounts of adjustments.

Improved rates and asymptotic normality for nonparametric neural network estimators

We obtain an improved approximation rate (in Sobolev norm) of r/sup -1/2-/spl alpha//(d+1)/ for a large class of single hidden layer feedforward artificial neural networks (ANN) with r hidden units and possibly nonsigmoid activation functions when the target function satisfies certain smoothness conditions. Here, d is the dimension of the domain of the target function, and /spl alpha//spl isin/(0, 1) is related to the smoothness of the activation function. When applying this class of ANNs to nonparametrically estimate (train) a general target function using the method of sieves, we obtain new root-mean-square convergence rates of Op([n/log(n)]/sup -/(1+2/spl alpha//(d+1))/[4(1+/spl alpha//(d+1))])=op(n/sup -1/4/) by letting the number of hidden units /spl tau//sub n/, increase appropriately with the sample size (number of training examples) n. These rates are valid for i.i.d. data as well as for uniform mixing and absolutely regular (/spl beta/-mixing) stationary time series data. In addition, the rates are fast enough to deliver root-n asymptotic normality for plug-in estimates of smooth functionals using general ANN sieve estimators. As interesting applications to nonlinear time series, we establish rates for ANN sieve estimators of four different multivariate target functions: a conditional mean, a conditional quantile, a joint density, and a conditional density. We also obtain root-n asymptotic normality results for semiparametric model coefficient and average derivative estimators.

A Heuristic Search Procedure for Detecting Sudden Shifts in Stationary Time Series Data

A new heuristic search procedure is proposed for retrospectively detecting shifts (defined as sudden changes in the process mean) within a stationary time series subject to substantial white noise. After identifying the first, most significant shift, the search procedure is applied progressively to detect further shifts and also to define the timing, size and statistical significance of such shifts. Prior to the application of the procedure, the time series under review is evaluated to determine whether it is consistent with the shifting-mean model that underlies the heuristic. A feature of the search procedure is that it can be operated automatically, with searches terminated either when the segment of the data series within which the next identified shift occurs is shown not to be suitable for the application of the heuristic, or when the latest identified shift proves not to be statistically significant.

A Heuristic Search Procedure for Detecting Sudden Shifts in Stationary Time Series Data

A Heuristic Search Procedure for Detecting Sudden Shifts in Stationary Time Series Data

A Heuristic Search Procedure for Detecting Sudden Shifts in Stationary Time Series Data

A Heuristic Search Procedure for Detecting Sudden Shifts in Stationary Time Series Data

Multivariate autoregressive time semes modeling: one scalar autoregressive model at-A-time

Multivariate (or interchangeably multichannel) autoregressive (MCAR) modeling of stationary and nonstationary time series data is achieved doing things one channel at-a-time using only scalar computations on instantaneous data. The one channel at-a-time modeling is achieved as an instantaneous response multichannel autoregressive model with orthogonal innovations variance. Conventional MCAR models are expressible as linear algebraic transformations of the instantaneous response orthogonal innovations models. By modeling multichannel time series one channel at-a-time, the problems of modeling multichannel time series are reduced to problems in the modeling of scalar autoregressive time series. The three longstanding time series modeling problems of achieving a relatively parsimonious MCAR representation, of multichannel stationary time series spectral estimation and of the modeling of nonstationary covariance time series are addressed using this paradigm.

A Heuristic Search Procedure for Detecting Sudden Shifts in Stationary Time Series Data

A new heuristic search procedure is proposed for retrospectively detecting shifts (defined as sudden changes in the process mean) within a stationary time series subject to substantial white noise. After identifying the first, most significant shift, the search procedure is applied progressively to detect further shifts and also to define the timing, size and statistical significance of such shifts. Prior to the application of the procedure, the time series under review is evaluated to determine whether it is consistent with the shifting-mean model that underlies the heuristic. A feature of the search procedure is that it can be operated automatically, with searches terminated either when the segment of the data series within which the next identified shift occurs is shown not to be suitable for the application of the heuristic, or when the latest identified shift proves not to be statistically significant.

A Theory of Reactor Diagnosis in Feedback Systems

A unified theory is presented for diagnosis of power reactors with feedback mechanism. In terms of correlation functions calculated from stationary time series data, a feedback system can be expressed by an equivalent innovation model. From the formalism the identifiability of open loop transfer functions in the feedback system is discussed under conditions; (1) the minimum phase system, (2) the independence of noise sources. From the feedback structure, the property of the nonminimum phase is related to that the reactivity is positive or zero-power reactor transfer function is supercritical. In the case of the nonminimum phase and correlated noise sources, there is a possibility of new additional loops in an innovation model equivalent to the feedback system.

A Theory of Reactor Diagnosis in Feedback Systems.

A unified theory is presented for diagnosis of power reactors with feedback mechanism. In terms of correlation functions calculated from stationary time series data, a feedback system can be expressed by an equivalent innovation model. From the formalism the identifiability of open loop transfer functions in the feedback system is discussed under conditions; (1) the minimum phase system, (2) the independence of noise sources. From the feedback structure, the property of the nonminimum phase is related to that the reactivity is positive or zero-power reactor transfer function is supercritical. In the case of the nonminimum phase and correlated noise sources, there is a possibility of new additional loops in an innovation model equivalent to the feedback system.