Differencing

# Differencing - Moving Average model weighted average of...

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Differencing (makes the variance the same...another way instead of log transform) Xt - X(t-1) = D(Xt) = rt drift=delta=trend component slope is delta the trend line is delta(T) line xt = delta t + sigma(Wi) Var (xt) = Var (delta t + sigma(Wi)) = Var( sigma (Wi)) = t * Var (Wi) = t * sigma^2 because delta t is a constant...does not have variability Var ( X + Y) = Var (x) + Var (Y) if x and y are independent (since there is no covariance) previous MA was used for in sample only...to see how the data did, this is more for forecasting ARIMA - Autoregressive I (differencing) Moving Average wt is stochastic which means it is random (white noise) Autoregressive model [AR(p)] autoregressive model with order p doing a regression on the past assuming we know the past few days, we can forecast the future
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Unformatted text preview: Moving Average model weighted average of past news (noise/errors) the covariance between the same lags is the same throughout in a time series f(x1, x2, x3) = f(xt+1, xt+2, xt+3) the covariance between x1 and x3 is the same as xt+1 and xt+3 i.i.d, the sample you get follows the same distribution and they are independent time series analysis → analyzing the data so we can take out the dependent residuals when you have a random walk, the variance increases over time dependent because tomorrow depends on where you are today compute a difference (gets rid of the dependency) D(Xt) = Xt - X(t-1) = rt …. rt is independent the variability of D(xt) is constant...
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