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2.1: Оцінка середнього
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=\ frac {1} {n^2}\ sum_ {s=1} ^nx_t\ праворуч) =\ frac {1} {n^2}\ sum_ {s=1} ^nx_1} n\ sum_ {t=1} ^n\ mathrm {Cov} (x_s, x_t)\\ [.2см] Якщо процес «близький до гауссіанності», то\[ \sqrt{n}(\bar{X}_n-...=\ frac {1} {n^2}\ sum_ {s=1} ^nx_t\ праворуч) =\ frac {1} {n^2}\ sum_ {s=1} ^nx_1} n\ sum_ {t=1} ^n\ mathrm {Cov} (x_s, x_t)\\ [.2см] Якщо процес «близький до гауссіанності», то $\sqrt{n}(\bar{X}_n-\mu)\sim AN(0,\tau_n^2), \qquad \tau_n^2=\sum_{h=-n}^n\left(1-\frac{|h|}{n}\right)\gamma(h). \nonumber$ $\gamma(h)=E[X_{t+h}^cX_t^c]=E\big[(\phi X_{t+h-1}^c+Z_{t+h})X_t^c\big]=\phi E[X_{t+h-1}^cX_t^c]=\phi\gamma(h-1)=\phi^{h}\gamma(0) \nonumber$