chapt2 - autocorrelation estimate at lag k, r k t=1 N-k (x...

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Time series of the day
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Stat 153 - 11 Sept 2008 D. R. Brillinger Simple descriptive techniques Trend X t = α + β t + ε t Filtering y t = r=-q s a r x t-r Simple moving average s = q , a r = 1/(2q+1) Filters may be in series
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Differencing y t = x t - x t-1 = x t "removes" linear trend Seasonal variation model X t = m t + S t + ε t S t S t-s 12 x t = x t - x t-12 , t in months
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Stationary case,
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Unformatted text preview: autocorrelation estimate at lag k, r k t=1 N-k (x t- )(x t+k- ) over t=1 N (x t- )2 autocovariance estimate at lag k, c k t=1 N-k (x t- )(x t+k- ) / N x x x x x Departures from assumption s Nonstationarity Trend - OLS Seasonality - trig functions Missing values Outliers...
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chapt2 - autocorrelation estimate at lag k, r k t=1 N-k (x...

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