If a time series is second order stationary, does this imply it is ...
WEBA process is second order stationary if its mean is constant and its autocovariance function depends only on the lag. Therefore does second order stationary imply strict stationary? Also under second order stationary it says that no assumptions are made about higher moments than those of first and second order.
Why does a time series have to be stationary? - Cross Validated
WEBDec 13, 2011 · 2. Time Series is about analysing the way values of a series are dependent on previous values. As SRKX suggested one can difference or de-trend or de-mean a non-stationary series but not unnecessarily!) to create a stationary series. ARMA analysis requires stationarity.
What is a second order stationary process? - Cross Validated
WEBThe class of linear time series models, which includes the class of autoregressive moving-average (ARMA) models, provides a general framework for studying stationary processes. In fact, every second-order stationary process is either a linear process or can be transformed to a linear process by subtracting a deterministic com- ponent.
Making a series stationary, 1st and 12th order differencing
WEBApr 15, 2020 at 12:39. If you have a series which has both a trend and a seasonal effect, then you would need a first order difference to elimate the trend and a 12th order difference to eliiminate seasonality if the data is monthly. The rcode might look something like diff (diff (name, lag=1,diff=1), lag=12,diff=1).
Trend stationary and difference stationary simultaneously
WEBJan 5, 2017 · 1 Answer. It certainly is possible that we may have a process that has both a deterministic time trend and a unit root, for example: yt = δt +y +ut. with ut being white noise, ut ∼ WN(0,σ2u). To achieve second-order stationarity in the above case, we first subtract the first lag from both sides (and we do not apply the Diferrence operator ...
How to make a time series stationary? - Cross Validated
WEBAug 24, 2010 · 53. Besides taking differences, what are other techniques for making a non-stationary time series, stationary? Ordinarily one refers to a series as "integrated of order p" if it can be made stationary through a lag operator (1 − L)PXt (1 − L) P X t. time-series.
time series - Moving average process - Cross Validated
WEBMar 9, 2019 · A moving average process of order (with finite), MA(q) is defined as: yt = ϵt + α1ϵt − 1 + α2ϵt − 2 + ⋯ + αqϵt − q, ϵt ∼ (0, σ2), and is for all the values of αj. So, in your example it is true that the variance and covariances change, but you can check that both are finite and do not depend on t (the covariance will depend ...
Whether a AR (P) process is stationary or not? - Cross Validated
WEBedited Jun 4, 2016 at 12:21. zahypeti. 117 4. asked Dec 13, 2011 at 21:24. user3125. 3,089 5 28 37. For an AR process to be stationary the roots of the AR polynomial must be outside the unit circle. Thus if the model is an AR (1) the coefficient must be absolutely less than 1.0 . All AR processes are not stationary.
time series - Stationarity of AR (p) process - Cross Validated
WEBApr 12, 2019 · 2. I'm looking for a proof for the stationarity of an AR (p) process, I know a stationary process Yt must fulfill the following conditions: (1) - E(Yt) = m for all values of t. (2) - Var(Yt) = σ2 for all values of t. (3) - cov(Yt, Ys) = γ(| t − s |) for every t and s. First I'll define an AR (p) process Yt as follows:
A proof for the stationarity of an AR (2) - Cross Validated
WEBConsider a mean-centred AR (2) process Xt = ϕ1Xt − 1 + ϕ2Xt − 2 + ϵt where ϵt is the standard white noise process. Just for sake of simplicity let me call ϕ1 = b and ϕ2 = a. Focusing on the roots of the characteristics equation I got z1, 2 = − b ± √b2 + 4a 2a The classical conditions in the textbooks are the following: {| a | <1 ...