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04_ts_chap2

# 04_ts_chap2 - Outline Variation Stationarity Time plot...

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Outline Variation Stationarity Time plot Transformations Trend Seasonal variation ACF Simple Descriptive Techniques Haipeng Xing, AMS316, Stony Brook University Outline Variation Stationarity Time plot Transformations Trend Seasonal variation ACF Outline 1 Types of variation 2 Stationary Time Series 3 The Time Plot 4 Transformations 5 Analysing Series that Contain a Trend 6 Analysing Series that Contain Seasonal Variation 7 Autocorrelation and the Correlogram Haipeng Xing, AMS316, Stony Brook University

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Outline Variation Stationarity Time plot Transformations Trend Seasonal variation ACF Types of Variation Seasonal variation Other cyclic variation Trend Other irregular fluctuations Haipeng Xing, AMS316, Stony Brook University Outline Variation Stationarity Time plot Transformations Trend Seasonal variation ACF Stationary Time Series The idea of stationarity: A time series is said to be stationary if there is no systematic change in mean (no trend), if there is no systematic change in variance and if strictly periodic variations have been removed. Much of the probability theory of time series is concerned with stationary time series, and for this reason time-series analysis often requires one to transform a non-stationary series into a stationary one so as to use this theory. The non-stationary components, such as the trend, may be more interesting than the stationary residuals. Haipeng Xing, AMS316, Stony Brook University
Outline Variation Stationarity Time plot Transformations Trend Seasonal variation ACF The Time Plot The plot of the observations against time is called a time plot , which will show up important features of the series such as trend, seasonality, outliers and discontinuities. The choice of scales, the size of the intercept and the way that the points are plotted may substantially a ff ect the way the plot ’looks’. The usual rules for drawing ’good’ graphs should be followed: A clear title must be given, units of measurement should be stated and axes should be properly labelled. Haipeng Xing, AMS316, Stony Brook University Outline Variation Stationarity Time plot Transformations Trend Seasonal variation ACF Example: The Time Plot Figure 1: Annual CPI, U.S. (1860–1970) Source: Hipel and Mcleod (1994).

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