Questions tagged [time-series]

This tag is used for question related to time series models such as AR, ARMA, ARCH, GARCH and their properties and techniques used for inference.

A time-series model is one which postulates a relationship amongst a num- ber of temporal sequences or time series. An example is provided by the simple regression model

$$y(t) = x(t) \beta + \epsilon(t)$$

or more commonly,

$$y(t) = \sum_{i=1}^p \phi_i y(t-i)+ \sum_{i=1}^k \beta_i y(t-i)+\sum_{i=1}^q \mu_i \epsilon(t-i)$$

965 questions
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How can I find the presample states of an AR model?

I have a question about the presample states of an ARMA model. Let assume that we have an AR(2) model $$x_t=\alpha_0 + \alpha_1x_{t-1} +\alpha_2x_{t-2}. $$ If $t=1, t=2$, then $x_1,x_2$ states are = ??. I am using Matlab and the program has a…
F.F.
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Time series: $Y_t = X_t - \mu$ is $AR(2)$

A problem says: "there is a time series $Y_t = X_t - \mu$ $AR(2)$ ..." I'm a little bit lost here. If it's $AR(2)$, where are is the $x_{t-1}$ and $x_{t-2}$ terms?
dark blue
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Variance and autocovariance or process $W_t = Y_t-Y_{t-1}$ with $Y_t$ process AR(1)

I need to find the variance and autocovariance or process $W_t = Y_t-Y_{t-}$ with $Y_t = c + \phi_1Y_{t-1} + E_t$ an AR(1) process with $-1 < \phi_1 < 1$ I end up with the following calculation : \begin{align*} \gamma_k &= Cov(W_t, W_{t-k}) \\ &=…
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Derivation of Double (Brown) Exponential Smoothing

I am learning the double (Brown) exponential smoothing. Comparing to the simple exponential smoothing, the Brown exponential smoothing smooths the output sequence $Y_t$ twice, such that \begin{align} S^{(1)}_t &= \alpha Y_t +…
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Interpretting ar coefficient in arma proccess

I'm currently studying autocorrelation in Python and exploring the ArmaProcess module within the statsmodels.tsa.arima_process package. This module allows us to set the parameters ar and ma. When dealing with the ar parameter, if we want to consider…
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What is the definition of "periodicity of the data"?

I'm reading a research paper where it says. Here $m$ is the periodicity of the data (e.g., 12 for monthly series). I understand: There are twelve months in a year. So I suspect periodicity relates to the max value of the period before it…
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Why does AR(P) = MA(P)

I am working my way through lecture notes from an econometrics course taught at Ohio State University on time series analysis. The current set of notes I am on (https://www.asc.ohio-state.edu/de-jong.8/note2.pdf) discusses ARMA models. On page 2 the…
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Multivariate time series and machine learning.

I have a question relate to apply machine learning algorithm to time series data. Because time series data has the impact of "order time or sequence" (I am meaning that time indexing, for example: current sale was impacted by previous sales), so how…
Sherry
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Time series questions in R

Let $X_t$ be the process satisfying the following equation:$$X_t = \phi X_{t−1} + Z_t − \theta Z_{t−2},\,\theta > 0,$$where $Z_t$ is a white noise process. What conditions on $\phi$ and $\theta$ are required for this process to be stationary,…
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Is log of ETS(MNM) a ETS(ANA) model?

Given two time series models $ETS(MNM)$ and $ETS(ANA)$. If we replace $y_t $ by $\ln y_t $ in $ETS(MNM)$, is it true the model will become $ETS(ANA)$?
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Analyzing revenue and historical data to estimate profit

What is the approach to solve such a question, given that I need to simply analyze a dataset and express findings I find? Problem: I am given a dataset of everyday revenue for three children companies of ABC for the period of January 1, 2014 to…
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auto-covariance gamma function

I'm learning time series analysis and I'm a little confused as to how the auto-covariance of a time series dataset works. We define the auto-cov function of a time series as: $\gamma(h) = E[(Y_t - u_t)(Y_s - u_s)] \ \forall \ h = t-s $ Here t and…
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newbie time difference

good day! i need help and be guided on the right path here, i'm pretty sure i'm lost. im trying to compute for time diffrence for start time and end time manually versus automatic ex. online computation. start time =08:55 am end time =13:22 pm for…
newb31
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How to normalize time series data

Forgive me if I am using the wrong terminology. I am trying to graph how productive a machine is over time with incomplete data. I am polling the machine at a random interval and getting the total number of parts produced at that moment in time. …
cstrutton
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What is a time-invariant linear filter

I am a new student of time series analysis. Could someone explain to me the meaning of time-invariant linear filter in time series? I do not understand the explanation in wikipedia or the course literature. Thanks in advance.
Dreason94
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