Contents
What is a weakly dependent time series?
A (time) sequence of random variables is weakly dependent if distinct portions of the sequence have a covariance that asymptotically decreases to 0 as the blocks are further separated in time. …
What is the difference between strong stationary and weak stationary in time series?
This form of stationarity is called strong because it doesn’t assume any distribution. It only says the probability distribution should be the same. In the case of weak stationarity, we defined distribution by its mean and variance.
What does integrated of order 1 mean?
be integrated of order one, or I(1) – A stationary series without a trend is said to be. integrated of order 0, or I(0) – An I(1) series is differenced once to be I(0) – In general, we say that a series is I(d) if its d’th difference is stationary.
What is the definition of weak stationarity?
With autocovariance functions, we can define the covariance stationarity, or weak stationarity. Inthe literature, usually stationarity means weak stationarity, unless otherwise specified. Definition 2(Stationarity or weak stationarity) The time series{Xt, t∈Z}(where Zis theinteger set) is said to be stationary if(I)E(X2
When is a stationary time series a weakly dependent time series?
A stationary time series is said to be weakly dependent (WD) if xt and xt+h are. almost independent” as h increases without bound. For a CS time series, this corresponds to the correlation between xt and xt+h going to zero suciently quickly” as h!1.
Why is stationarity important in time series analysis?
This is just the first step in time series analysis. For the majority of algorithms, the series must be stationary, in order for the analysis and predictions to be performed. That’s the main reason why I think this step needs to be automated — it’s tedious to test many differentiation orders manually. Now you have the tools to proceed.
Do you need auto covariance for weak stationarity?
Weak stationarity only requires the shift-invariance (in time) of the first moment and the cross moment (the auto-covariance).