# 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.

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### Show that all series satisfy this equation $\sum_{\mid h\mid < n } \hat{\gamma}(h)=0$

I need to show that the sample autocovariance of the series {$x_1,...,x_n$} satisfies $\sum_{h<\mid n \mid}\hat{\gamma}(h)=0$ I start by defining $\bar{X}= \frac{1}{n}\sum_{t=1}^{n}X_{t}$ and that ...
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### How to estimate this (unusual?) model for a time series of covariance matrices?

I am wondering if anyone can point me to econometrics or statistics literature on estimating the covariance matrices of models of the following form. Or, if someone with enough domain knowledge would ...
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### Measuring variation of mean and variance in time series

I don't get how the variation of mean and $\sigma$ are measured for instance in the following picture from here: The red line is the mean of the data which changes. It is said that the standard ...
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### Time series dataset - averaged over five years [closed]

I have a dataset on daily accidents in a particular province from the years 2001-2005. I need to create a time series data set of daily accidents, averaged over five years. The way I'm thinking about ...
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### Analytical Wavelets

I'm trying to understand the difference between a Time-frequency analysis done with standard wavelet, and another done with analytical wavelet. If I take as a signal a function $f \in L^2(\mathbb{R})$ ...
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### Equations of a trendcpt model

After fitting a Trend cpt changepoint model to certain data using the EnvCpt library in R, the estimated parameters are: ...
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### Stationarity in seasonal time series

Given a time-series difference equation, how can I tell whether it's stationary or not? e.g. let's take $\phi_p(B)\Phi_P(B^s)=(1-0.2B^2)(1-6B^{12}+12B^{24})$ where seasonality=12, for the AR and ...
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### Ways to obtain networks from multivariate time-series

I recently became aware of a bridge between (dynamical) properties of time-series and (topological) features of an associated network representation. A variety of methods exist to embed the time-...
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### Unevenly spaced data

I'm working on a project that is made up of X-values (Julian dates) and Y-values (measurement data). My current problem is that the X-values have some dates that are too close together (let's say ...
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### Summability conditions for coefficients of the reciprocal of a power series

I wonder if there is some reference for materials like the following. Let $\frac{1}{\beta(z)}$ be well-defined for all z with $|z|\leq1$, where $\beta(z)=\sum_{k=0}^{\infty} \beta_kz^k$. Then, we ...
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### Does high standard error and high r-square imply spurious regression?

Does a regression passed on time series data with one independent variable and one dependent variable which yields parameters with very high standard errors (t-values) and also a high r-squared imply ...
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### Distribution of maximum of a moving average sequence

Let $Z_n \sim WN(0,\sigma^2)$ and $a \in \mathbb{R}$, $$X_t = Z_t + aZ_{t-1} \qquad t = 0, \pm1, \pm 2,...$$ defines a $MA(1)$ sequence. I need to prove that this sequence has an independent extremal ...
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### Which covariance matrix should I use for treating heteroskedasticity in my panel data?

I have a data set with panel structure (panel data) with 78 individuals observed over 5 three-year periods. I have 10 dependent variables an 1 independent variable. I applied logarithmic ...
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### Interpretation of graphs of ACF and PACF

I plotted graphs of ACF and PACF (in R), but I do not know, how to find out, which orders of differences are statistically significant. Could somebody explain it to me? I found on the Internet that "...
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### Time Series - ARMA$(1,1)$ Model

Consider the autocorrelation function of the ARMA$(1,1)$ process is given by $Y_t= \alpha Y_{t -1} +Z_t + \beta Z_{t-1}$. Show that $\text{Var}(Y_t) = \frac{1+\beta^2+2\alpha\beta}{1-\alpha^2}$. ...
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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 ...