The autoregressive (AR) model is a stochastic process modelling time series, which specifies the value of the series linearly in terms of the previous values.

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Individual versus group-wise significance in ARDL context

In an ARDL model approach, what is one supposed to do if the F-bound test shows insignificance while some variables have significant long run and short run coefficients (the error correction term is ...
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17 views

How to estimate a two-level, driven, AR(1) process

I would like to estimate the following model: $$ y_t = (1-a)\,y_{t-1} + a\,\mathbf{b}^T\mathbf{x}_t + \epsilon_t \\ z_t = (1-c)\,z_{t-1} + c\,y_{t} $$ where $z_t$ and $\mathbf{x}_t$ are observed, ...
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37 views

Vector autoregression: many variables (10), short sample (100)

Suppose there are ten observation sites along the road. A, B, C, D, E, F, G, H, I, J. We obtain data at each site once in a day, in this order. That is, first go to the site A at 9:00a.m., and when ...
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18 views

Sum of the AR coefficients and First Order Autocorrelation Coefficient

I'm working with quarterly inflation, usually a AR(4) and I want to obtain different measures of persistence, that are: 1. the sum of the AR coefficients Σα 2. First Order Correlation Coefficient, ...
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14 views

Combining continuous spatial and discrete time series methods for spatial prediction

Here's something I've been pondering. Wondering if anyone can shed come light on it/recommend some references/tell me why it makes no sense, please. In my field (predicting crime risk by location), ...
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25 views

Order of AR and MA

How to determine the order of AR and MA Process for the time series data of length 8000?? Also let me know how to find coefficients of AR and MA as the references provides only for a0 and a1...
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2answers
92 views

Periodicity and seasonality of a time series

I have a time series and I have done some spectral analysis on it. When doing an autocorrelation and periodogram it shows that the time series is periodic. However when I do a Dickey-Fuller test it ...
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39 views

How to calculate interim and long-run multipliers in ARDL models with >1 lag?

I have calculated an ARDL(24,36) model with 1 independent variable. The data is monthly, hence the inclusion of so many lags. I am trying to calculate the interim multiplier (the cumulative effect at ...
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24 views

How can I test for seasonality when the trend is not supposed to be monotonic but sinusoidal?

My knowledge of time-series analysis is limited. So far I have only assessed whether there was a seasonality in my time series data with the assumption of monotonic trend. To test that I would have ...
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17 views

How to fit Autoregressive model with 2 lags on dataframe with missing values and multiple columns in R

I have a dataframe with 4000 companies, each company present as a column in the dataframe. The complexity of my dataframe is that companies belong to a stock exchange and all companies that had been ...
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19 views

Reproducing an AR Model

I recently found this paper https://static.googleusercontent.com/media/www.google.com/en//googleblogs/pdfs/google_predicting_the_present.pdf where the authors predict economic trends with Google ...
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52 views

Mitigate autocorrelation in time series with AR(2) process

I have a dataframe with 4000 companies and I have calculated a liquidity measure of each of the company in the dataframe. Liquidity is highly persistent. And my analysis shows that in these indiviual ...
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2answers
114 views

Time series with autoregressive distributed lags: Forecasting for future

I have daily data from last 2 years. I want to do ARIMAX and the regressor component being autoregressive distributed lag of the same variable. Since it has impact, along with dummy variables to ...
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17 views

How to write this ARIMA model mathematically? [duplicate]

I am trying to analyze a time series: I see a strong seasonal pattern, so from every value, I subtract the value from the same month the previous year (12 periods prior). Also, I am using 1 AR term ...
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2answers
54 views

Time series analysis (ACF, PACF)

I have this monthly time series with pronounced seasonality and a bit of trend: The ACF and PACF for 4 years (48 months) are: Can I suppose that the data don't need transformations like: ...
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1answer
177 views

Does using lagged independent variables makes sense?

While it seems quite common to calculate a lagged version of the dependent variable and to use it on the right hand side of a model (e.g., autoregressive models), I have rarely seen that lagged ...
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23 views

How to interpret linear filter formula

I am taking my first course in time-series analysis, and I recently encountered the so-called linear filter for the first time. I thought I could just skip this section. Apparantly though, this ...
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21 views

heteroscedastic time series in SAS autoreg - white noise matter?

I normally work with categorical outcomes, so a lot of this is new to me. Attempting to model monthly interrupted time-series in proc autoreg. There were 11 intervention changes of varying potency ...
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27 views

Generate multivariate time series

Suppose that I want to generate tri-variate Gaussian time series $\{(X_{1i}, X_{2i}, X_{3i}), i=1,2,...,n\}$ with a correlation structure across the three time series; that is, $(X_{1i}, X_{2i}, ...
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16 views

Suitable Estimator for Panel ARDL

Any body knows what are suitable estimators available to estimate panel ARDL(p,q) with N = 6 & T = 48? I tried to use mean group and pooled mean group estimator by Pesaran and Shin (1999) by ...
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5 views

Generate sample process with CrossSectional Correlation and autoregressive structure

How can you generate a sample multidimensional time series $X_{t,i}$ for $t \in \{1,2,...,T\}$ and $i \in \{1,2,...,M\}$ where: $E[X_{t,i}] = 0$ $E[X_{t,i}X_{t,j}] = \Sigma_{i,j}$ ...
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29 views

Does Auto-correlation cause AR(p) model?

This is the autocorrelation case. $y_{t}=X_{t}B+u_{t}$ where $u_{t}=\rho u_{t-1}+e_{t},$ $e_{t}$ is iid From this autocorrelated disturbances, I might be able to say $y_{t}=\gamma ...
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1answer
51 views

Fitting model AR(1) with R

I've sampled 100 variables from a Gauss distribution with mean 0 and standard deviation 1. > set.seed(1) > wn=rnorm(100) Then I've fitted an AR(1) model ...
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1answer
57 views

AR model with vector valued variables (in R)

I want to estimate a vector-valued model $$\mathbf{y}_t = a\mathbf{y}_{t-1}+b\mathbf{y}_{t-2}+\cdots$$ Here, each $\mathbf{y}_t\in\mathbb{R}^n$ and the coefficients $a,b,\dotsc$ are real numbers ...
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1answer
17 views

Is it redundant to use moving average AND auto-regressive terms in an ARIMA model?

Seems to me they are by the following equation: $$(1-\phi_1B)(1-B)X_t = (1-\theta_1B)\epsilon_t$$ We could just divide both sides by $1-\theta_1B$ and not ever have to deal with lagged error? I'm ...
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16 views

CFA model with systematic temporal correlation between measures

I'm looking to fit CFA models to data in the case where measures have systematic temporal correlations between them. I'm familiar with autoregressive approaches, such as those described on Dave ...
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37 views

Unbiased estimator for AR($p$) model

Consider an AR($p$) model (assuming zero mean for simplicity): $$ x_t = \varphi_1 x_{t-1} + \dotsc + \varphi_p x_{t-p} + \varepsilon_t $$ The OLS estimator (equivalent to the conditional maximum ...
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2answers
79 views

What's wrong if I fit the auto-regression with OLS?

I am doing auto-regress by usual linear regression package. e.g. $y_t=φx+ε_t$ with $x =y_{t-1}$ My reason is that, Auto-regression does assumes iid errors, same for linear regression. Linear ...
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1answer
84 views

Can ARIMA be used to forecast trend in time series data?

I am new to ARIMA. I have a time series data that has a negative trend.I need to predict its value for the upcoming time period. I know that one of the steps in ARIMA is to de-trend data through ...
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41 views

Estimator for AR(1) process

Consider an AR(1) process $X_{t+1}=cX_t+\epsilon_t,$ where $|c|<1$, and $\epsilon_t\sim N(0,\sigma^2)$ are i.i.d, and $X_0$ a fixed constant. I am looking for a reference for the following fact: ...
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1answer
30 views

Criterion for model selection in an AR model?

I would like to smooth some financial time series data under the assumption that the data consists of variable trend and cyclic components plus white noise. I am thinking of applying an AR model to ...
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40 views

Autocorrelated Returns?

I'm trying to compute some VAR models for the Amgen Pharmaceutical company (NasdaqGS: AMGN), however I've noticed that the daily returns seem to be significantly autocorrelated at a number of lags ...
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16 views

Autocorrelation function decay for AR(p), how to proof

How can I demonstrate that the Autocorrelation function (ACF) for an AR(p) decay exponentially? It seems so simple but neither Enders' book nor Greene's has such proof.
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46 views

Generate a random variable which follow Gamma distribution and AR(1) process simulatenously

Is it possible to generate numbers from Gamma distribution (with parameters shape=10, scale=15, say) which also follow a AR(1) process, simultaneously? If it's possible, than how to do that?
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135 views

Auto-regression versus linear regression of x(t)-with-t for modelling time series

What difference precisely does autoregression (for AR(p), p=1,2,...) have when compared to linear regression of that time series random variable w.r.t time axis? Explanation with diagrams clarifying ...
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16 views

How are the regime parameters estimated in Threshold Autogressive (TAR) models?

I am looking to implement a TAR model in Matlab and I am confused about the estimation technique. Take for example the stock return on S&P 500. So here is what I know so far: 1. Set threshold, ...
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26 views

Conditional covariance of AR(1)

I am trying to derive the conditional covariance of an AR(1) process, $\text{Cov}(y_t,y_{t+h})$. I have been trying to solve it taking in account the law of iterated expectations (LIE). However, I ...
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141 views

Lag length selection in a dynamic model, ARDL approach to cointegration in R

I want to programme an ARDL approach to cointegration in R. Below is the generic equation: $$\Delta y_t=\beta_0+\sum \beta_i \Delta y_{t-i}+\sum \gamma_k \Delta x_{1,t-k}+\sum \psi_j \Delta ...
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45 views

Breusch-Godfrey Test and the length of the lag, p

I'll use Breusch-Godfrey (BG) test to test correlation of an AR(1) model. In order to perform a BG test, the simple regression model is first fitted by ordinary least squares to obtain a set of sample ...
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34 views

Multicollinearity in Auto Regressive models

I have just started learning about time series analysis. I had a doubt regarding AR models. I understand that in Auto Regression, we regress one variable on values of the same variable at different ...
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18 views

Handling non-normality in the residuals of a spatial autoregressive model

I am performing a spatial autoregressive model (function errorsarlm in spdep R package). Although I tried a number of alternative variables transformations, the model' residuals are always non-normal. ...
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36 views

Derivation of conditional expectation and variance of the AR(1) process

I have a question regarding the AR(1) process. I want to derive the conditional expectation $E(X_{(t)}| X_{(0)})$ and the variance $\operatorname{Var}(X_{(t)}|X_{(0)})$ of the AR(1) process: ...
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22 views

Stable VAR($p$) procress: Is there an easy way to do this?

Assume a $K$-dimensional VAR($p$) process given by $$y_t=\nu+A_1y_{t-1}+\ldots+A_py_{t-p}+u_t$$ This process is called stable if the roots of the reverse characteristic polynomial are bigger than 1 in ...
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201 views

conditional vs unconditional forecast variance in AR(1)

I have trouble showing that conditional forecast error of AR(1) has smaller variance than the unconditional one. I can show that cond. forecast error is: $$ Y_{T+1}=aY_{T}+\epsilon_{T+1} $$ $$ ...
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1answer
59 views

AR.OLS isn't matching to an OLS on the autoregressive lags, Why?

I am using R and running ar.ols() on some data. And trying to compare to a more "manual" method of computing an AR model by doing lm() using the autoregressive lags as my independent variables. ...
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1answer
34 views

AR(4) - show E(Yt) = 0

I was wondering if anyone could help me show that $E(Y_t) = 0$? I have had a go myself but have got stuck. Could someone please point me in the right direction? Consider the stationary AR(4) model ...
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11 views

MATLAB and Spectral Density function

I have simulated an AR(1) process in MATLAB with this code ...
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1answer
121 views

Spectral density function of AR(1) process

I'm studying the derivation of the spectral density function of an AR(1) process. Starting from its autocovariance function, we have that: $$\gamma_0 = \frac{\sigma^2}{1-\alpha_1 ^2}$$ and $\gamma_k ...
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32 views

Is this a Poisson GLM problem? or OLS? Predicting Counts for a future window of time

Say I have one day's worth of a GIANT food court's order data whose per minute order distribution looks like this (1440 mins in the day): But the catch is that the food court is comprised of, say, ...
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73 views

Training auto.arima() in R

I have around 10000 time series and I want to train ARIMA model using 8000 of them. I wanted to use auto.arima function http://www.inside-r.org/packages/cran/forecast/docs/auto.arima however I am ...