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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Time series analysis - Identifying the model

A time series given by following $$X_{t-3} – 2.5X_{t-2} + 2X_{t-1} – 0.5X_{t} = E(t) $$ Can you fit an $\text{ARIMA}(p,d,q)$ model in this ? I tried bring the $X(t)$ term on the right hand side and dividing the entire equation by its coefficient…
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Cointegration: Why is rank deficiency necessary?

Consider the error correction form for the vector time series $Y_t$: $\Delta Y_t = \Pi Y_{t-1} + \Phi_1 \Delta Y_{t-1} + ... + \Phi_p \Delta Y_{t-p} + \epsilon_t$. Here, $Y_t$ are non-stationary and $I(1)$. Clearly, all terms except the $\Pi…
balaks
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Determining the number of parameters when calculating AIC and BIC

I currently have the following formulas: $AIC = \ln(\sigma^2)+2(p+q+1)/T$ $BIC = \ln(\sigma^2)+ln(T)(p+q+1)/T$ This does not work for every $ARMA(p,q)$ model. How do I amend the formula depending on the number of parameters?
Haych
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Finding time series mean variance skewness of stationary time series

Given a model for a stationary time series $r_t$, written as: $r_t=\epsilon_t$ and $\epsilon_t=\sqrt{h_t} z_t$, where $z_t$ follows $N(0,1)$ and $h_t$ is some positive random variable, which is independent of $z_t$. Is the mean of $r_t=0$ and …
hefq
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Defining a known time series in R

Is it possible to define time series like $X_t = 0.2X_{t-1}-0.48X_{t-2}+Z_t $, $Z_t \sim WN(0,\sigma^2)$ in R and then analyze it - for example plot its ACF and PACF? I can only find information on how to turn data into a time series and analyze…
Win
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How do you make a single time series from 3 separate non overlapping time series in R?

my goal is to create a simulated time series composed of three time series each with the same $p,d,q$ but with different standard deviations then fit an arima (which will not fit by design). i.e i want to make a heteroskedastic time series in…
Nuala
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Time Series (White Noise)

$\newcommand{\Cov}{\operatorname{Cov}}$Suppose $\{W_t\}$ and $\{Y_t\}$ are two independent normal white noise series with $\operatorname{Var}(W_t)=2\operatorname{Var}(Y_t)=4$. Let $X_t = W_t-0.5W_{t-1}$ and $Z_t=Y_t+0.4Y_{t-1}-0.4Y_{t-2}$. Put…
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Linear Regression with lagged dependent variable question

this is my first time posting here so I hope I get everything right. I'm taking a basic course on linear regression but don't really understand a problem I've come across. In fact, I don't understand a lot of problems I've come across. Thing is,…
ains21
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What weak stationarity tells use about the variance.

As a start, I'm sorry if I utilize some of these terms terribly, as I'm very unfamiliar with this field. If a series yt,yt-1, ... is weakly stationary. What would this tell use about limit of var(yt) as t approaches infinity? I found something that…
tinyhippo
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Autocorrelation function.

Let $X = (X_t : t ∈ Z)$ be a $MA(1)$-Process. Define the time series $Y = (Y_t : t ∈ Z)$ with $Y_t = \mathbb 1_{(X_t > 0)}$. What is the Autocorrelation function of $Y_t$? Anyone has any idea how to even start solving this? There was a hint to show…
WaitForIt
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How to reproduce time series from simple moving average

For a time series $X = \{X_1, X_2, ...\}$, knowing its n-period simple moving average $SMA = \{SMA_n, SMA_{n+1}, ...\}$, where $SMA_m = {X_m + X_{m-1} + ... + X_{m-(n-1)}\over n}$. How to reproduce time series $X$ from $SMA$, if n is 30?
roger
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Gaussian filter: Which scales are smoothed for a given sigma?

I do have (I hope!) a simple question. Let's say I have a time series with a discretization of "$dt$" (in real world: yearly values in my specific case). Now I use a Gaussian Filter with $\sigma = 4$, which gives me a half-width of about ~ $6*dt$…
Balinus
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Modeling Financial Time Series

Price time series are not stationary. So we difference them and get the return time series, which are stationary. Does this mean, it is always a good idea to model only the return series of financial assets. Alternatively, do we not need to model…
square_one
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Calculate the hours to reach from source to destination?

Assume that source = A Destination = b distance between A to B is 100 mile . QUESTION 1 If a vehicle runs at the speed of the distance remaning then how many hours it will take to reach destination [assume vehicle starts at the speed of…
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Predictive model of time series

I have a set of $n$ objects where an object, $n_x$, consists of two time series lists of numbers. ${n_1, n_2, n_3,...,n_n}$ where $n_x={2,3,4,1,3,5,34,...},{4323,23,42,34,1,1,1,...}$. For each $n_x$ object, time series one has been shown to be…