Questions tagged [unit-root]

A unit root is a property of a non-stationary time series which can lead to spurious regressions and wrong inference.

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statsmodels.adfuller weird behaviour of usedlag value

I'm learning about time-series analysis and have two series on which I'm performing an Augmented Dickey-Fuller test in order to check for stationarity. I'm trying to understand why I get very ...
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Examining stationarity, mean and variance of time series

Hi guys, I encounter this question for a Business Forecasting module and I am very confused by it. Firstly, this looks like an autoregressive model of order 1. From the looks of it, the φ coefficient ...
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Does the Absence of a Unit Root Imply Wide Sense Stationarity?

I'm taking a course on time series currently and have been slightly confused about the interplay between unit roots and stationarity in a question I've been attempting to answer. The question set up ...
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Phillip-Perron test - sample size requirement?

I understand that both Phillips-Perron and Augmented Dickey Fuller tests are for the presence of a unit root in a time series. It is my understanding that these test conduct those tests differently, ...
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How is this series possibly stationary (by ADF Test)? [duplicate]

Here is an attached image of a time series that I am testing for stationarity using the Augmented Dickey-Fuller test. Here is the command I ran in R: ...
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What to do when kpss contradicts ADF?

I'm testing to see if Inflation has a unit root and if it has a drift and trend, just drift or no drift and trend. My results from the ADF test looks like this: ...
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Current best practices for detecting Unit Root in time series data?

I'm trying to get an overview of what are the current best practices for detecting unit roots in time series data. The main approach I came across is the Augmented Dickey Fuller (ADF) test, which ...
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Normalizing ARIMA(0,2,q) generator

I'm doing simulations of an ARIMA(0,d,q) process, and confused about the scaling when d=1 vs d=2. Using a series of random terms $e_t \sim N(0,1)$: I generate $Y_{d1}$ ~ ARIMA(0,1,0) as $y_t = y_{t-1}...
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Panel-data unit-root tests (xtunitroot vs. dfuller)

I have 120 IDs. For each ID I have hourly data (90 hours per ID). My data is perfectly balanced. I run xtunitroot tests and all the different versions (llc, ips, demean, trend, lags etc.) and I ...
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Variance and empirical distribution

We know that regressing two I(1) time series that are not cointegrated might give rise to spurious results. Indeed, we might have an excess of rejection of the null hypothesis due to the fact that as ...
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Time-Series: Testing for stationarity and random walks

My goal is to test the weak-form efficient market hypothesis using time-series on prices of various stocks listed on S&P 500. According to theory, a particular stock is said to be weak-form ...
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Ur.df interpretation

I have been working on and reading about the ur.df test in R, so I know what the tests mean, what the hypotheses are and how to read the critical values. (For ...
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Is HEGY or CH test better in a small sample (40 monthly observations)?

I have a time series of monthly data that is 40 observations ($3\frac{1}{3}$ seasonal cycles) long. HEGY test and CH test give contradicting results w.r.t. presence of a seasonal unit root. HEGY test ...
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Seasonal differencing a when the sample size is small when estimating a VAR

When estimating a VAR the series must be level and seasonally stationary. However I have only 48 data points. I first made the series level stationary based on the ADF test and performed HEGY test for ...
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Unit root MA process

A unit root AR process blows up because white noise is accumulated. Does a unit root MA process also blow up? How can a unit root MA process be stationary, for example, when it can be expressed with ...
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Understanding Dickey-Fuller Test vs. t-test

I am working to understand why it is that in an AR(1) regression, the regression coefficient is not asymptotically t-distributed. Specifically, I'm trying to understand which assumptions about a ...
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How to interpret results of a Dickey-Fuller test?

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Non Gaussian ARMA and invertibility of the process

There are many ARMA(p,q) processes, with different parameter values, associated with the same auto-correlation function. If this processes are also Gaussian, this implies they follow same exact ...
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Are unit roots of a MA(q) process a problem?

If I understand this answer correctly, it is not a problem for a Gaussian ARMA(p,q) process to be non-invertible (ie some of the roots of the MA part of the process are inside or on the unit circle). ...
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Does a constant term in a nonstationary AR model always imply a trend?

Given an $AR(k)$ model of the form $$y_t = \alpha_1y_{t-1}+...+\alpha_ky_{t-k} + \mu + \varepsilon_t$$ with $\alpha$ satisfying $(1-\alpha_1 z - ... -\alpha_k z^k ) = 0$ for $z=1$, does a nonzero $\mu$...
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What can and can’t you say about a series with a unit root as evidenced by an ADF test? [duplicate]

I have a time series with 500+ observations which has a unit root, as evidenced by an ADF test at the sub 1% significance level. I want to explain to my class mates why that’s important and change the ...
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Can there exist a unit root series that’s Granger-caused, or better predicted with a model other than the AR process we tested using ADF?

If a series has a unit root, then it is a function of random white noise. Therefore, it follows a random walk process. Is it then possible for: Some other series to Granger-cause the unit root series?...
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ADF test estimates -0.01 delta, but the p-values are less than 0.05

I am dealing with two datasets of Annual growth Production Cost, and Annual growth Inflation. A lot of problems have arisen, but the most annoying one is referred to integration. At first sight, both ...
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KPPS stationary test [duplicate]

KPSS accepts the null hypothesis at 1%, but not at 5% or 10%. Could someone explain this to me please? KPSS statistic: 0,1524 Critical values: 1% 0,2160, 5% 0,1460 y 10% 0,1190. can I assume trend ...
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The contradiction in KPSS and HEGY test

I am new to this field and I have a question. I have a seasonal rainfall dataset and I want to apply SARIMA model on it. For this purpose, I applied the KPSS tests and I got the following output: <...
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How to interpret the HEGY test?

I performed the HEGY test on the level stationary data to test for any seasonal unit roots. Given below is my output. Should I conclude that there exists unit roots based on the output since F11_12 is ...
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Struggling with the intuition behind unit roots of time series variables

I have been taught that to determine if an autoregressive process is stationary you: Express the process in lag polynomial notation. Replace the lag operator by a variable (let's call it z), and set ...
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How to deal with a mix of I(1) and I(2) variables?

I have one dependent variable which becomes stationary after the first difference I(1). There are 4 independent variables, out of which 2 become stationary after the first difference and the other two ...
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Vector error correction models and order of integration

I am trying to estimate VEC models for three variables in different regions. So, using each region's data I am estimating a different VEC model. Mostly, series are I(1) and co-integrated. To have ...
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VAR Model with different integration order

I am trying to create a VAR model with 4 variables. 3 of them need 2 differences in order to be stationary, while 1 needs only 1. When I take differences I loose one row of data, so there is one ...
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Cointegrated panel data but stationary regressor

I have a panel with 50 years and 97 countries. I plan to do cointegration with a methodology which requires all regressors to be I(1), but one of them is actually I(0). I looked at individual ...
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Basic question about interpreting ADF test results

These are results from ADF test as implemented in the aTSA package in R: ...
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Augmented Dickey Fuller test, determining the number of lags used

In a paper by Mark P. Taylor he conducts ADF tests on exchange rates and he describes the determination of lag number with "The number of lagged dependents that we need to include to induce ...
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Random-walk and unit root processes predictable?

I know that a random walk is an AR(1) with a unit root, but there are also higher order autoregressive processes with unit roots. Does the unit root in such a higher order autoregressive process also ...
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How to choose "Integrated of order" for time series data?

My data series becomes stationary at 2nd difference but it is also stationary at 1st difference only with inclusion of trend or constant term. So, what Integrated of order should I choose 1 or 2?
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Which is the original source for the Augmented Dickey Fuller test?

Which paper first introduces the Augmented Dickey Fuller (ADF) test? Wikipedia does not mention any particular citations this paper (#1 on google scholar when searching for the test) does not ...
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Express an I(2) process as a sum of telescoping cumulative sums

Suppose $z_t$ is zero mean I(2) process Show that $z_t$ can be written as $$z_t = \sum_{i=1}^t e_i +\sum_{i=1}^{t-1}e_i +\sum_{i=1}^{t-2}e_i +...+e_1 $$ where $e_i$ is white noise process.
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Stationarity test for count data time series

can someone give me an overview of stationarity test for time series of count data? For instance, I would like to know if there exists a test similar to the Augmented Dickey Fuller or how this test ...
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VAR in levels of differences when series are integrated but not cointegrated?

I have monthly financial time-series data from 2011-present of four stock market indices. I conducted various stationarity tests and found that the series are I(1) processes (stationary only in first ...
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Augmented Dickey-Fuller test null rejected. AR(1) in ARCH(1) p-value of 0.000

I am trying to model the logged returns of 5 different markets. When running the the Augmented Dickey-Fuller (ADF) tests on the logged market returns, the p-value is 0.000 for all markets regardless ...
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unit-root test for unbalanced multivariate panel data [closed]

I want to conduct unit root test for my unbalanced multi-variate panel data. I use only R studio. I saw many helpful posts on Stata and EViews but I am seeking solutions for RStudio only, please. I ...
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Making an AR(3) model weakly stationary

I have a model as:$$r_t=0.05+\frac{7}{6}r_{t-1}+\frac{1}{6}r_{t-2}-\frac{1}{3}r_{t-3}+a_t$$ When checking for stationarity: $$1-\frac{7}{6}x-\frac{1}{6}x^2+\frac{1}{3}x^3=0$$ I get $x\in \{-2,1,1.5\}$....
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Normality of tau-statistics ($\tau_{\mu}$ and $\tau_{\tau}$) in presence of unit roots

The original Dickey-Fuller (1979) paper, considers three regressions ($(1.1), (2.1)$ and $(2.2)$) but only two DGP ($1.1$ and $2.1$), while deriving the limiting distributions. The paper defines three ...
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R: Panel unit root test with unbalanced data due to late entry into the sample

I would like to conduct a panel unit root test on the price constituents of the Dow Jones Industrial Index, which is composed of 30 stocks. The index spans 20 years, and stocks drop out of the index ...
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How to add both long-term and short-term interest rates as variables for a GARCH model?

I was facing some difficulties with a model of mine. I want to look up how the portfolio reacts to interest rate changes and I would like to use a GARCH model. However, both the short-term and long-...
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MA(q) unit roots

I'm looking at this statement: "Similarly, an MA(1) model is said to have a unit root if the estimated MA(1) coefficient is exactly equal to 1. When this happens, it means that the MA(1) term is ...
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Do more general specifications of Dickey Fuller lead to bias if true model is more parsimonious?

When I was studying econometrics I was taught that whenever in doubt it is always better to run more general specification both in terms of including drift term or trend term and including lags, as ...
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Reference Request: Book on Unit Root Theory

In trying to do time series analysis, I almost regularly stumble upon unit root and cointegration tests. The design of most these tests is based on a null of unit root (for both linear and non-linear ...
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If $y_t$ and $x_t$ are cointegrated, then are $y_t$ and $x_{t-d}$ also cointegrated?

Assume that $x_t, y_t$ are $I(1)$ series which have a common stochastic trend $u_t = u_{t-1}+e_t$. Particularly, consider the following DGP \begin{align} y_t&=\alpha_y+u_t+a_t \tag{1} \\ \end{...
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4 votes
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Influence of Seasonality on Unit root tests

I gather from this question and answer, a seasonal series is non-stationary as its mean depends on which month it is. Suppose I have a series which possibly has a unit root (stochastic trend) but also ...
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