this is for holding javascript data
Jack O'Brien edited untitled.tex
almost 8 years ago
Commit id: e051f51dfe243e961e88e95f56905e9e17ea2e18
deletions | additions
diff --git a/untitled.tex b/untitled.tex
index 5eb0389..0a697c0 100644
--- a/untitled.tex
+++ b/untitled.tex
...
\subsection{ARMA}
**Talk about using white noise to drive the process
There exist a class of finite difference equations used in the analysis of discrete time series known as autoregressive-moving average (ARMA) processes.
These equations relate Given any autocovariance function $\gamma(h)$ for which $\lim_{h\to\infty}\gamma(h) = 0$ and for any integer $k > 0$, there exists an ARMA(p,q) process with autocovariance function $\gamma_X(h)$ such that $\gamma_X(h) = \gamma(h)$ for all $h \leq k$. This makes the ARMA process a very useful tool in the
autoregressive analysis and
moving average properties modeling of
a times series. (obvious) time-series. A stationary process $\{X_t\}$ is an ARMA(p,q) process if at every time $t$
$$X_t - \phi_1X_{t-1} - ... - \phi_pX_{t-p} = Z_t + \theta_{t-1} + ... + \theta_qZ_{t-q} $$