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# Time Series Notes (6) - Parameter estimation

Residual Analysis Definition of residuals Consider an $\text{AR}(1)$ model with a constant term: $Z_t=\phi Z_{t-1}+\theta_0+a_t$, having estimated $\phi$ and $\theta_0$, the residuals are defined...

# Time Series Notes (5) - Parameter estimation

Introduction The hyper parameters of a time series model, for example, $p,d,q$ for an $\text{ARIMA}(p,d,q)$ model is already known. And the model will be completely determined if the values of par...

# Time Series Notes (4) - Model specification

Model-building strategy Box-Jenkins method for model-building strategy graph TD A([Start with a time series realization]) --&gt; B[Identify a preliminary time series model] --&gt; C[Estimat...

# Time Series Notes (1) - Fundamental concepts

What is time series? Defintion of times series A time series is stochastic process in discrete time, that is a sequence of random variables ${Z_t}$, which are ordered by a time index $t$. Two ch...