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How do I solve this? How can I obtain the lag-one autocorrelation coefficients just from the data??

Following are $10$ years of observation of annual streamflows in millions of cubic meters:

$$\begin{array}{|c|cl|}\hline\hline \text{Year}&1&2&3&4&5&6&7&8&\\\hline\text{Discharge}&145.78&95.43&116.66&96.12&122.09&175.02&101.98&146.14\\\hline \text{Year}&9&10\\\hline\text{Discharge}&126.01&132.73 \end{array}$$

Use the above data to estimate the parameters of an first order Autoregressive model and the parameters of an first order Moving Average Model.

Argha
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Fung Chun Chun
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1 Answers1

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For AR(1)[i.e. first order Auto-regressive model] $U_t=\alpha U_{t-1}+\epsilon_t$ we know that

$\hat \alpha=r_1$=the auto-correlation of lag $1$

$\,\,\,\,\,=$The product moment correlation coefficient obtained from $(x_1,x_2),(x_2,x_3),\dots(x_{n-1},x_n)$

Here $n=10$.

Argha
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