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1autocorrelation

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Unformatted text preview: : (1)N: number of values. (2) △t: time interval. Time series analysis: detecting, describing, and modeling climate variability and impacts. Care must be taken when you work on a time series data. Aliasing: The information that varies at shorter timescales appears as information at longer timescales. (1) Auto‐correlation Auto‐correlation: The simple linear correlation of a time series with its own past; that is, the correlation between a variable A sampled at time t and the same variable A sampled at a later time t+△t, t+2Δt, .... Example Auto‐correlation between U(t) and U(t+1) Index: 0 1 2 3 4 5 6 7 8 9 Time: noon 1 2 3 4 5 6 7 8 9 pm U(t): 5 6 5 4 7 5 3 5 4 6 U (t+1) 6 5 4 7 5 3 5 4 6 Example Auto‐correlation between U(t) and U(t+1) Index: 0 1 2 3 4 5 6 7 8 9 Time: noon 1 2 3 4 5 6 7 8 9 U(t): 5 6 5 4 7 5 3 5 4 6 U (t+1) 6 5 4 7 5 3 5 4 6 U(t+1) Scatter plot of hourly wind speed versus the following hour’s wind speed U(t) rAB COVAR(A,B) AB U(t+1) Best visualization of autocorrelation is by plotting the autocorrelation as a function of lag time, that is autocorrelation function (acf). 1 U(t) U(t): 5 6 5 4 7 5 3 5 4 6 U (t+1) 6 5 4 7 5 3 5 4 6 Best visualization of autocorrelation is by plotting the autocorrelation as a function of lag time, that is autocorrelation function (acf). U(t): 5 6 5 4 7 5 3 5 4 6 U (t+1) 6 5 4 7 5 3 5 4 6 U(T+2) 5 4 7 5 3 5 4 6 12 Best visualization of autocorrelation is by plotting the auto‐ correlation as a function of lag time, that is autocorrelation function (acf). U(t), U(t+1); U(t), U (t+2); U(t), U(T+3);….. U(t), U(t+6);…… U(t), U(t+24);……… Acf: show the amount of persistence in time series. All acfs exhibit a decay with lag time. The time that it needs to make acf near 0 indicates the memory. Best visualization of autocorrelation is by plotting the auto‐ correlation as a function of lag time, that is autocorrelation function (acf). U(t), U(t+1); U(t), U (t+2); U(t), U(T+3);….. U(t), U(t+6);…… U(t), U(t+24);……… From statistics, autocorrelation can be established as U(t)=f1* U(t-1) + f2* U(t-2) + … Best visualizat...
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