Showing papers on "Partial autocorrelation function published in 1994"
Book•
21 Nov 1994
TL;DR: In this article, the authors present an alternative solution method for Deterministic Processes by iteratively solving homogeneous difference equation and finding particular solutions for deterministic processes, and conclude that the proposed solution is the best solution.
Abstract: PREFACE. ABOUT THE AUTHOR. Chapter DIFFERENCE EQUATIONS . 1 Time-Series Models. 2 Difference Equations and Their Solutions. 3 Solution by Iteration. 4 An Alternative Solution Methodology. 5 The Cobweb Model. 6 Solving Homogeneous Difference Equations. 7 Finding Particular Solutions for Deterministic Processes. 8 The Method of Undetermined Coefficients. 9 Lag Operators. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 Imaginary Roots and de Moivre's Theorem. Appendix 2 Characteristic Roots in Higher-Order Equations. Chapter 2 STATIONARY TIME-SERIES MODELS . 1 Stochastic Difference Equation Models. 2 ARMA Models. 3 Stationarity. 4 Stationarity Restrictions for an ARMA(p, q) Model. 5 The Autocorrelation Function. 6 The Partial Autocorrelation Function. 7 Sample Autocorrelations of Stationary Series. 8 Box-Jenkins Model Selection. 9 Properties of Forecasts. 10 A Model of the Interest Rate Spread. 11 Seasonality. 12 Parameter Instability and Structural Change. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 Estimation of an MA(1) Process. Appendix 2 Model Selection Criteria. Chapter 3 MODELING VOLATILITY . 1 Economic Time Series The Stylized Facts. 2 ARCH Processes. 3 ARCH and GARCH Estimates of Inflation. 4 Two Examples of GARCH Models. 5 A GARCH Model of Risk. 6 The ARCH-M Model. 7 Additional Properties of GARCH Processes. 8 Maximum Likelihood Estimation of GARCH Models. 9 Other Models of Conditional Variance. 10 Estimating the NYSE International 100 Index. 11 Multivariate GARCH. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 Multivariate GARCH Models. Chapter 4 MODELS WITH TREND . 1 Deterministic and Stochastic Trends. 2 Removing the Trend. 3 Unit Roots and Regression Residuals. 4 The Monte Carlo Method. 5 Dickey-Fuller Tests. 6 Examples of the ADF Test. 7 Extensions of the Dickey-Fuller Test. 8 Structural Change. 9 Power and the Deterministic Regressors. 10 Tests with More Power. 11 Panel Unit Root Tests. 12 Trends and Univariate Decompositions. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 The Bootstrap. Chapter 5 MULTIEQUATION TIME-SERIES MODELS . 1 Intervention Analysis. 2 Transfer Function Models. 3 Estimating a Transfer Function. 4 Limits to Structural Multivariate Estimation. 5 Introduction to VAR Analysis. 6 Estimation and Identification. 7 The Impulse Response Function. 8 Testing Hypothesis. 9 Example of a Simple VAR Terrorism and Tourism in Spain. 10 Structural VARs. 11 Examples of Structural Decompositions. 12 The Blanchard and Quah Decomposition. 13 Decomposing Real and Nominal Exchange Rate Movements An Example. Summary and Conclusions. Questions and Exercises. Endnotes. Chapter 6 COINTEGRATION AND ERROR-CORRECTION MODELS . 1 Linear Combinations of Integrated Variables. 2 Cointegration and Common Trends. 3 Cointegration and Error Correction. 4 Testing for Cointegration The Engle-Granger Methodology. 5 Illustrating the Engle-Granger Methodology. 6 Cointegration and Purchasing-Power Parity. 7 Characteristic Roots, Rank, and Cointegration. 8 Hypothesis Testing. 9 Illustrating the Johansen Methodology. 10 Error-Correction and ADL Tests. 11 Comparing the Three Methods. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 Characteristic Roots Stability and Rank. Appendix 2 Inference on a Cointegrating Vector. Chapter 7 NONLINEAR TIME-SERIES MODELS . 1 Linear Versus Nonlinear Adjustment. 2 Simple Extensions of the ARMA Model. 3 Regime Switching Models. 4 Testing For Nonlinearity. 5 Estimates of Regime Switching Models. 6 Generalized Impulse Responses and Forecasting. 7 Unit Roots and Nonlinearity. Summary and Conclusions. Questions and Exercises. Endnotes. STATISTICAL TABLES. A. Empirical Cumulative Distributions of the tau. B. Empirical Distribution of PHI . C. Critical Values for the Engle-Granger Cointegration Test. D. Residual Based Cointegration Test with I (1) and I (2) Variables. E. Empirical Distributions of the lambda max and lambda trace Statistics. F. Critical Values for beta 1 = 0 in the Error-correction Model. G. Critical Values for Threshold Unit Roots. REFERENCES. SUBJECT INDEX.
6,714 citations
TL;DR: The modification of Pollard et al's test was the best test for detecting delayed density dependence in series of abundances per generation.
Abstract: I investigated the ability of statistical tests to detect delayed density dependence in series of abundances per generation. I generated time series containing delayed density dependence using two simple population models (a host-parasitoid model and a version of the Ricker equation) and analysed these using the tests for delayed density dependence of Turchin (1990), the lag 2 partial autocorrelation coefficient (PACF) and a novel modification of Pollard et al's (1987) test. All tests of delayed density dependence are of low statistical power, and so any delayed density dependence that is present may frequently be overlooked, particularly with short (< 25 generation) time series. The modification of Pollard et al's test was the best test for detecting delayed density dependence
36 citations
TL;DR: The authors derive necessary and sufficient conditions for consistency in mean square of an estimator, which are in the form of a single sum of autocorrelation coefficients, in the forms of a double sum of Autocor correlation coefficients, and in the bifrequency domain and in terms of the average spectrum.
Abstract: The cyclic autocorrelation is often used to describe nonstationary random processes. The authors investigate the conditions under which the cyclic autocorrelation can be estimated consistently in mean square for discrete time Gaussian processes. They extend and generalize results of Hurd (1989) and refine results of Boyles and Gardner (1983). They derive necessary and sufficient conditions for consistency in mean square of an estimator, which are in the form of a single sum of autocorrelation coefficients, in the form of a double sum of autocorrelation coefficients, in the bifrequency domain and in terms of the average spectrum. They also discuss the rate of convergence for this estimator. >
31 citations
TL;DR: In this article, the autocorrelation parameter σ is studied in nonparametric and semiparametric regression models with autoregressive errors and it is shown that under mild assumptions one can construct an estimator that is asymptotically equivalent to the least squares estimator based on the autoregression error process.
29 citations
TL;DR: This topic is revisited and, introducing a new matrix link coefficient between two random vectors, a general framework for estimating the PACF is given, leading to new autoregressive estimation methods based on sample estimators of the partial autocorrelation coefficients.
17 citations
TL;DR: In this article, the authors investigated the effects of autocorrelation and other time-series effects for the frequently advocated supplementary runs rules for both individual control charts based on the moving range and sample standard deviation, using simulation.
Abstract: The basic assumption underlying statistical control chart criteria is that the process measurements are independent and identically distributed over time. However, autocorrelation and other time-series effects occur frequently in application. In this paper, the effects of autocorrelation are investigated for the frequently advocated supplementary runs rules. For both individual control charts based on the moving range and sample standard deviation, using simulation, the impact of autocorrelation for the AR(1) on in-control average run lengths is given.
12 citations
TL;DR: This paper discusses the behavior of sample estimates of the inverse autocorrelation function for overdifferenced series and describes this pattern as a specific pattern that occurs when an analyst mistakenly differences a stationary series.
Abstract: . Differencing is often used to render a time series stationary. The decision of how much differencing to do is usually based on plots of data, the autocorrelation function or a statistical test. Hence, it may happen that an analyst mistakenly differences a stationary series. When that happens, the inverse autocorrelation function takes on a specific pattern. We characterize this pattern and discuss the behavior of sample estimates of the inverse autocorrelation function for such overdifferenced series.
12 citations
1 Dec 1994
TL;DR: In this article, the authors derive the asymptotic distribution that turns out to be closely related to the Dickey-Fuller (1979) distribution and discuss the behaviour of the sample autocorrelations of integrated MA(1) and AR(1).
Abstract: In case of a random walk the theoretical autocorrelations tend to one asymptotically. The sample autocorrelations, however, may decline rather fast even with large samples. We will explain this observation by deriving the asymptotic distribution that turns out to be closely related to the Dickey-Fuller (1979) distribution. Moreover we discuss the behaviour of the sample autocorrelations of integrated MA(1) and AR(1) processes. In order to prove our results we consider more general I(1) processes and apply the functional central limit theorem injected to time series analysis by Phillips (1987). We obtain unit root tests that are based on autocorrelation estimators of higher lags. We discuss their finite sample behaviour experimentally.
10 citations
TL;DR: In this article, an autocorrelation function method was developed for estimating the parameters of autoregressive models, where an ordinary least-squares method was used to optimally determine the parameters by minimizing the sum of the squares of differences between the autocorerelations calculated directly from the observed time series and those from the model-generated streamflow.
Abstract: An autocorrelation function method was developed for estimating the parameters of autoregressive models. For monthly streamflow series, an ordinary least-squares method was used to optimally determine the parameters by minimizing the sum of the squares of differences between the autocorrelations calculated directly from the observed time series and those from the model-generated streamflow. The approach was tested using numerical simulation and historical data. Numerical results showed that for some generated data series the parameters estimated by the new method were closer to their true values than those obtained from the Yule-Walker equations. For monthly streamflow time series of three stations of Yellow River in China, the historical correlation functions were compared with those from data series generated with the AR(2) model. The autocorrelation function estimated from the generated data series was closer to the observed autocorrelation than that obtained from the Yule-Walker equations. This is even more true for the multivariate autoregressive model.
10 citations
TL;DR: Partial autocorrelation function (PACF) of a stationary two-dimensional separable process is defined in this paper, and properties of the sample PACF are derived and used in identifying the orders of a spatial autoregressive process.
6 citations
Journal Article•
TL;DR: In this paper, a case study using actual daily stream records to model and forecast the daily stream discharge at a temporary causeway designed for bridge pier construction is presented. And the use of the model to refine the design of temporary structures and to assess the risk of overtopping is evaluated and discussed.
Abstract: Daily stream discharge generated by an Autoregressive Model is helpful in the design and risk assessment of temporary riverine construction projects. This case study uses actual daily stream records to model and forecast the daily stream discharge at a temporary causeway designed for bridge pier construction. With autocorrelation and spectral density functions, the stream flow trend and deterministic cycles can be identified and separated. With partial autocorrelation function, the persistency of the stream flow can be determined in stochastic terms. Finally, using the autoregressive process, a stream flow forecast model can be established. The use of the model to refine the design of temporary structures and to assess the risk of overtopping will be evaluated and discussed. This case study will conclude with a comparison between actual stream flow data and the model's forecasted discharge.
TL;DR: In this article, an autoregressive process is proposed to model time series data with multiple observations at each time point, and the joint autocorrelation function for the model has a product form, the first factor being the autocore correlation function for a stationary AR( p ) process and the second factor involving a constant intraclass correlation ρ.
1 Jan 1994
TL;DR: In this article, a time series of monthly minimum temperatures and their monthly averages (1961-84) from Guadalajara (Spain) have been analyzed by the Box-Jenkins method.
Abstract: A time series of monthly minimum temperatures and their monthly averages (1961–84) from Guadalajara (Spain) have been analyzed by the Box-Jenkins method. The ARIMA model obtained was identical for both temperature series: (1 0 0) (0 1 1)12 N. The aim of our work has been to study a method of calculating an index of freezing based on time series analysis, and try to predict the probability of this situation.
31 Dec 1994
TL;DR: Robust statistical approaches to the problem of discriminating between regional earthquakes and explosions are developed and it is noted that signal discrimination approaches based on discrimination information and Renyi entropy perform better in the test sample than conventional methods based on spectral ratios involving the P and S phases.
Abstract: : Robust statistical approaches to the problem of discriminating between regional earthquakes and explosions are developed. We compare linear discriminant analysis using descriptive features like amplitude and spectral ratios with signal discrimination techniques using the original signal waveforms and spectral approximations to the log likelihood function. Robust information theoretic techniques are proposed and all methods are applied to 8 earthquakes and 8 mining explosions in Scandinavia and to an event from Novaya Zemlya of unknown origin. It is noted that signal discrimination approaches based on discrimination information and Renyi entropy perform better in the test sample than conventional methods based on spectral ratios involving the P and S phases. Two techniques for identifying the ripple-firing pattern for typical mining explosions are proposed and shown to work well on simulated data and on several Scandinavian earthquakes and explosions. We use both cepstral analysis in the frequency domain and a time domain method based on the autocorrelation and partial autocorrelation functions. The proposed approach strips off underlying smooth spectral and seasonal spectral components corresponding to the echo pattern induced by two simple ripple-fired models. For two mining explosions, a pattern is identified whereas for two earthquakes, no pattern is evident.
27 Jun 1994
TL;DR: In this article, an almost surely consistent estimate of the order of an autoregression from estimates of the partial autocovariance coefficients is given, where the coefficients are derived from the partial auto-correlations.
Abstract: The paper shows how to obtain an almost surely consistent estimate of the order of an autoregression from estimates of the partial autocovariance coefficients. >
TL;DR: Some structural properties of certain vector generalizations of second-order functions of a stationary stochastic process based on determinantial functions of autocovariances are discussed and a duality property is found.
Abstract: . Some structural properties of certain vector generalizations of second-order functions of a stationary stochastic process based on determinantial functions of autocovariances are discussed. In particular, a generalized autocovariance function which retains all properties of the ordinary autocovariance function is considered and the linear dependence structure of certain scalar stochastic processes associated with this function is investigated. Properties of the normalized function are discussed and a duality property is found, according to which this function also generalizes in a natural way the ordinary partial autocorrelation function of stochastic processes.