The Analysis Of Time Series: Theory And Practice

1.Introduction 1.1Examples 1.2Terminology 1.3Objectives 1.4Approaches to time-series analysis 1.5Review of time-series literature. 2.Simple descriptive techniques 2.1Types of variation 2.2Stationary time series 2.3Time Plot 2.4transformations 2.5Analysing series wchich contain a trend 2.5.1Curve-fitting 2.5.2Filtering 2.5.3Differencing 2.6Seasonal fluctuations 2.7Autocorrelation 2.7.1The correlogram 2.7.2Interpreting the correlogram 2.8Other test of randomness.exercise. 3.Probability models for time series 3.1Stochatic processes 3.2Stationary processes 3.2.1Second-order stationary 3.3The autocorrelation function 3.4Some useful stochastic processes 3.4.1A purely random process 3.4.2Random walk 3.4.3Moving average processes 3.4.4Autoregressive processes 3.4.5Mixed models 3.4.6Integrated models 3.4.7The general linear process 3.4.8Continuous processes 3.5The wold decomposition theorem.Exercise. 4.Estimation in the time domain 4.1Estimating the autocovariance and autocorrelation functions 4.1.1Interpreting the correlogram 4.1.2Ergodic theorems 4.2Fitting an autoregressive process 4.2.1Estimating the parameters of an autoregressive process 4.3Fitting a moving avarage process 4.3.1Estimating the parameters of a moving average process 4.3.2Determining the order of a moving average process 4.4Estiamting the parameters of mixed model 4.5Estimating the parameters of an integrated model 4.6The Box-Jenkins seasonal model 4.7Residual analysis 4.8General remarks on model bulding. Exercise. 5.Forecasting 5.1Introduction 5.2Univariate procedures 5.2.1Extrapolation of trend curves 5.2.2Exponential smooothing 5.2.3Holt-Winters forecasting procedure 5.2.4Box-Jenkins forecasting procedures 5.2.5Stepwise autoregression 5.2.6Other methods 5.3Multivariate procedure 5.3.1Multiple regression 5.3.2Econometric models 5.3.3Box-Jenkins method 5.4A comparison of forecasting procedures 5.5Some examples 5.6Prediction theory. Exercises. 6.Stationary processes in the frequency domain 6.1Introduction 6.2The spectral distribution function 6.3The spectral density function 6.4The spectrum of a continuous process 6.5Examples.Exercise. 7.Spectral analysis 7.1Fourier analysis 7.2A Simple sinusoidal model 7.2.1The Nyquist frequency 7.3Periogram analysis7.3.1The relationshipbetween the periodgram and the autocovariance function 7.3.2Properties of the periodogram 7.4Spectral analysis :some consistent estimation procedures 7.4.1 Transforming the truncated autocovariance function 7.4.2Hanning 7.4.3Hamming 7.4.4Smoothing the periodogram 7.4.5The fast fourier tranform 7.5confidence intervals for the spectrum 7.5Confidence intervals for the spectrum 7.6A comparison of different estimation procedures 7.7Analysing a continuous time series 7.8discussion 7.9An example.Exercise. 8.Bivariate processes 8.1Cross-coveriance and cross-correlation functions 8.1.1Examples 8.1.2Estimation 8.1.3Interpretation 8.2The cross-spectrum 8.2.1Examples 8.2.2Estimation 8.2.3Interpretation. Exercise. 9.Linear systems 9.1Introduction 9.2Linear system in the time domain 9.2.1Some examples 9.2.2The impulse response function 9.2.3The step response function 9.3Linear system in the frequency response function 9.3.2Gain and phase diagram 9.3.3Some example 9.3.4General relation between input and output 9.3.5Linear system in series 9.3.6Design of filters 9.4Identification of linear systems 9.4.1Estimating the frequency response function 9.4.2The Box-Jenkins approach 9.4.3Systems involving feedback. Exercise. 10.Some other topics

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