Mathematics Stack Exchange
Mathematics Stack Exchange

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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RSI indicator and smoothing technic

In this article RSI formula is given as follows: RSI = 100 - 100/(1 + RS) where RS = (average gain)/(average loss) First Average Gain = Sum of Gains over the past 14 periods / 14 First Average Loss = Sum of Losses over the past 14 periods /…
David Johns
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arima model forecast using out-of sample values

suppose I have n+m sample data. I constructs a arima model using first n sample points. Can I fix the arima model then predict m periods forwardly so as to get the last m predictions. the residuals of the last m sample points are calculated as the…
lee james
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Why is this AR(2) causal?

Consider a strictly stationary ARCH(2) process $X_t = \sigma_tZ_t,$ $t \in \mathbb{Z}$, with iid standard normal noise $(Z_t)$ where $\sigma^2_t=\alpha_0+\alpha_1 X^2_{t-1} +\alpha_2 X^2_{t-2} ,$ $\alpha_i>0,i=0,1,2$. Assume that $E[\sigma_0^4] <…
lemon
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t stats in ADF test for unit root

I am dealing the ADF test process, and find the limit distribution of t stats. The context is, $(y_t)$ is given by \begin{equation}\label{eq1} y_t = \mu + y_t^0 \end{equation} and $(y_t^0)$ is generated as $y_t^0 = \alpha y_{t-1}^0 + u_t$. $(u_t)$…
Chris
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In what book can I learn the mathematical theory of times series?

In what book can I learn the mathematical theory of times series? I know times series is always taught in statistics courses, so a lot of other mathematical fields may omit this in their textbooks.
Victor
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Forecasting using LSTM network

I have a time series data of size 150. I trained 80% (120 data points) and tested the remaining 20% (30 data points) of the data set by LSTM network. So I got the predicted values of the series from 121 st to 150 th. I just used the code given in…
sameer poongadan
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Time series regression - any tips?

I have a time series where $y_t > y_{t-1} 95\%$ of the time. It’s autocorrelation function is such that it’s decreasing (yt is most correlated with 1 lagged period. This is obvious from looking at it since it looks as if $y_t = y_{t-1}+$ (a small…
blanchey
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Creating monthly time series from yearly means

I have a yearly time series which is the following: 1 2008 1.423832 2 2009 4.017000 3 2010 11.333000 4 2011 10.840000 5 2012 15.324000 6 2013 9.822000 7 2014 5.065000 8 2015 11.759000 9 2016 3.260000 10 2017 11.517000 11 2018…
zest16
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Estimate variance of AR(2) using Yule-Walker method

We have a AR(2) process $$X_t-\mu=\phi_1(X_{t-1}-\mu)+\phi_2(X_{t-2}-\mu)+\epsilon_t,$$ where $\epsilon_t$ is a white noice process, and I got $$\hat{\phi_1} = \hat{\rho}(1)\frac{1-\hat{\rho}(2)}{1-\hat{\rho}^2(1)}$$ and $$\hat{\phi_2} =…
VincentN
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Time series with same autocovariance function

If two time series have the same autocovariance function, are they the same process? For me, this holds only if we suppose that the errors $\epsilon_t$ are normal, because in that case, the resulting $x_t$ are normally distributed and their joint…
Victor
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ARMA (1,2) model - Auto covariance function

I am struggling with finding the Autocovariance function $\gamma(k)$, of the following ARMA(1,2) model: $x_t-0.9x_{t-1}=e_t+2e_{i-1}+0.5e_{t-2}$. I have already found this model to be stationary, hence the auto-cov. will only depend on the…
Jonathan Kiersch
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How to implement Kalman filter when state vector contains observable and unobservable variables?

The problem is as follows: in a state space model: \begin{align} S(t) &= A * S(t-1) + u(t) \\ Z(t) &= B * S(t) + v(t) \end{align} where $S(t)$ is a vector process containing $4$ variables but only the last $2$ variables are unobservable, $Z(t)$…
Victor
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Causal and non causal AR(1) process

Assuming you have the following $AR(1)$ process, $X_t=\phi X_{t-1}+\epsilon_t$, where $\{\epsilon_t\}$ is a white noise sequence and $|\phi|>1$, it is easy to find that the non-causal solution is $X_t=\sum_{i=1}^\infty -\phi^{-i}\epsilon_{t+i}$.…
Daniel Ordoñez
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Determine stationary solution ARMA(2,1)

We consider the time series ARMA(2,1): $X(t)-0.75X(t-1)+0.5625X(t-2)=Z(t)+1.25Z(t-1)$ Does $\{X(t)\}$ have stationary solution? Give the form of the solution. At first we are looking for the roots of autoregressive polynomial. None of them is on…
SigmaMat
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Finding the impulse reponse function with a cubic shock

I have the following time series $$x_t = \epsilon_t + a \epsilon_{t-1}^3,$$ where $0
user3889486
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