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# TS_P1 - INTRODUCTION TO TIME SERIES ANALYSIS A time series...

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1 INTRODUCTION TO TIME SERIES ANALYSIS A time series is a series of observations generated sequentially over time or space Example: Day (t) Return (y t ) 1 2.0 2 2.5 3 2.6 4 2.9 5 3.0 Underlying stochastic process {Y t } = {Y 1 , Y 2 ,... } Time series analysis = methods for analyzing time series.

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2 Goals of time series analysis Describe (model) systems accurately Explain or give reasons for the patterns observed Predict the behavior of systems Control the behavior of systems Plan and carry out activities efficiently and effectively = °±²²³°° !
3 Time domain and Frequency domain analyses Time domain analysis = analysis based on actual data {Y t } ° main tool of analysis = Auto-correlation function Frequency domain analysis = analysis based on data that has been transformed to complex numbers { ° j = A j +iB j =R j e ij ± } ° main tool of analysis = spectrum (periodogram)

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4 Modeling time series Model = verbal/mathematical/statistical description of a system’s movements Types Models: ² Deterministic = one whose trajectory is completely determined by initial (boundary) conditions [not subject to error] X t =X 0 e 2t X t = 5 +2t + 10cos(2 ³ t/12) ² Stochastic [Probabilistic] = one whose trajectory depends on chance [subject to error] X t = X 0 e 2Wt where W t is the value of a (normal) random at time t, [e.g. value of a government security such as a bond].
5 Main types of variation/components of a time series Trend (T t ) = a systematic short or long term movement/variation [a] deterministic trend e.g. ´ (t) = 5+2t [b] stochastic trend e.g. Y t = Y t-1 + e t Seasonal [periodic] (S t ) = recurs with a fixed frequency i.e. at regular intervals of time e.g. such as mean monthly rainfall, mean

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