Time series are data observed over time (either in continuous time or at discrete time periods).

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X11 deseasoning: too few datapoint for S3x3 moving average?

Do I have too few data points to use a $S_{3\times3}$ moving average? I have the following dataset for January months, ...
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59 views

Marketing Data with many zeros

I am working on a marketing data which is a time series data with marketing spend done through different channels and revenue generated. The data looks like this : My data contains too many zeros ...
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9 views

Deciding the lag while testing for timeseries data stationarity

I am currently reading up on time series forecasting using ARIMA in SAS. I just began to go through what has been explained here : ...
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39 views

Do we need to detrend when do Cross-Correlation between two time series?

I have a group of time series variables and I want to found out the relationship among them. The method I use is to calculate pair-wise correlation between two time series and found out those with ...
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2answers
42 views

AR(2) model is causal

AR(2) model is : $$X_t=\phi_1X_{t-1}+\phi_2X_{t-2}+W_t$$ Where $W_t\sim N(o,\sigma^2)$ I want to prove AR(2) model is causal . So , I tried as : $$X_t-\phi_1X_{t-1}-\phi_2X_{t-2}=W_t$$ ...
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43 views

Modeling Time-Series with a lower bound

I am trying to fit a model to a time series that has a lower bound (at around -150). Using an ARIMA model, running simulations often leads to the time series hitting (and going underneath) this lower ...
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2answers
53 views

Linear correlation between two sets of data

I have various data sets that correspond to values (in percentage) at given time points (hours, up to 10 hours). The total number of data sets of values at given time points is 8. My question is ...
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34 views

Getting an error message “Error in if(reached.threshold < min.reached.threshold)…” while training network using neuralnet package

I'm using R to create train and test a neural network on a time series (the annual sales of a company over a large period of time). As using the package's default learning algorithm (resilient ...
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38 views

Dealing with nonstationarity and autocorrelation

Relationship between interest rates and retail sales. I have a time series sample of quarterly data for 10 years. My dependent variable is retail prices and independent variables are interest rates, ...
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26 views

Sampling Distribution of Sample Correlation Coefficient

For a linear process $X_t=\mu+\sum_j\varphi_jW_{t-j}$ where $W_t$ is white noise and $\mathbb E(W_t^4)<\infty$ , $$ \begin{pmatrix} \hat\rho(1) \\ \hat\rho(2) \\ \vdots \\ ...
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Hodrick-Prescott Filter, Time Series, SDE, and Ito Isometry

The background of this question is a paper written by Morten O.Ravn and Harald Uhlig, titled "On Adjusting The Hodrick-Prescott Filter For The Frequency of Observations" Consider the decomposition of ...
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24 views

Eviews and Forecasting Linear Regression with AR(1) Error Term

This question is geared towards those who are familiar with Eviews and forecasting with linear regression in the case of AR(1) error terms. Consider the classical linear regression model where the ...
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19 views

EWMA or Moving Average when Estimating Trend in Seasonal Data

What is generally the best practice when estimating trend (non-seasonal component) in seasonal data? Centred Moving Average as suggested by MatLab docs Averaged EWMA (backwards & forwards) as ...
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18 views

Making a Time-series Stationary: Order of Operations

Following various sources including this post, which is the correct approach to making a time-series stationary? Remove trend Remove seasonality or Remove seasonality with estimated trend ...
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12 views

Comparing Variance Ratio tests to Hurst exponents

I have used the Chow Denning test and the Hurst exponent (Peng, Whittle and R/S methods) to examine if a particular time series follows a random walk. My results are conflicting between the 2 tests. ...
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26 views

Which is the best way to check (with some certainty) if the mean of a time series is a constant?

I am testing the time series output by a light sensor, and trying to know when dawn and dusk end. I used a cusum test to check when light level starts changing, and now I need to know when it ...
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1answer
18 views

Comparison of time series models

I'm trying to create a model for a series $X = \{X_1, X_2, ...\}$. I don't assume that the $X_i$ are identical distributed nor that they are independent but at least that they have something in common ...
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22 views

Stationarity of time series data

The following are plots of the original data first order difference values of original data and the first order difference of the log transformed data. Can someone please tell me which of 2 and 3 ...
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3answers
46 views

Exactly The Same Autocovariance Function of Two Time Series

A MA(2) process : $$X_t=W_t+\frac{5}{2}W_{t-1}-\frac{3}{2}W_{t-2}$$ where $\{W_t\}\sim WN(0,1)$ And another MA(2) process : $$X_t=W_t-\frac{1}{6}W_{t-1}-\frac{1}{6}W_{t-2}$$ where $\{W_t\}\sim ...
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29 views

Why does randomising the order of measurements remove time as a confounding variable?

Say we're interested in the difference in x between Group1 and Group2. We might measure 50 samples from Group1 then 50 samples from Group2. If the accuracy or precision of our measurements change over ...
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29 views

Autoregression for 20 numbers

If I had 20 numbers over a certain time period say 20 days and would like to figure out the next 5 numbers in the series, I am assuming I use an AR(20) Autoregression. However, I don't know how to do ...
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36 views

Seasonality in residuals [closed]

I'm running a simple OLS with two seasonally adjusted independent variables and the dependent variable is also seasonally adjusted. I'm seeing distinct seasonality in the residuals of the estimation. ...
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61 views

Correct procedures to detect and correct outliers for aggregated/SKU time series

Background I am currently working with sets of product sales time series at SKU-level for a FMCG company. Data are available in a weekly format for multiple years and sales data for hundreds of ...
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23 views

Valid Instruments for an IV/2SLS Regression for house prices

I'm brand new here so my apologies if this is too general or has been answered elsewhere. I'm trying to estimate a model for the house prices that includes several endogenous regressors. For the sake ...
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1answer
69 views

Anomaly detection in time series data

Hi I have a large data set of objects, each containing a list of the same attributes. The data is arranged in a time series so that the value for an attribute for an object is indexed by its time. I ...
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3answers
45 views

Multilevel modeling for limited dependent variable

I am doing the research, using Multilevel modeling, with limited dependent variable number of days- it is limited downward (0) and upward (30). Is it necesarry to use Multilevel logit model? Or is it ...
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21 views

Which test do I need to apply for repeated measures?

My research question is as follows: How does on-ground presence of bird species A, B, and C change in relation to: 1. species A breeding chronology, and 2. time of day/month My data consists of ...
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5 views

Good way to “Lag” a time series in order to perform online analysis?

I have two irregular time series of data that I've been looking at. They correspond to irregularly spaced live updates on the vertical position of two flying objects in time. The probes installed in ...
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36 views

Autoregression Model

I am new to statistics and math in general as I started at such a late age. I am trying to come up with a model that can predict future numbers using past numbers based on multiple time series that ...
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1answer
49 views

What is the right algorithm to detect segmentations of a line chart?

To be concrete, given 2D numerical data as is shown as line plots below. There are peaks on a background average movement (with small vibrations). We want to find the values of pairs (x1, x2) if those ...
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1answer
21 views

How to calculate p values of long-run coefficients in autoregressive distributed lag (ARDL) bound test approach

For example, I estimate an ARDL with two variables as follows. D(xt) = a + D(xt-1) + D(yt-1) + xt-1 + yt-1 + e where D refers to first order difference. According to ARDL bound approach the long ...
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67 views

Can PCA be applied for time series data?

I understand that Principal Component Analysis (PCA) can be applied basically for cross sectional data. Can PCA be used for time series data effectively by specifying year as time series variable and ...
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34 views

Understanding results from Augmented Dickey Fuller test

I have no background in statistics/econometrics but some theory I'm applying to geophysics data requires the data to be stationary (or at least trend-stationary) and I don't believe they are. I've ...
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1answer
39 views

ACF of MA(2) with constant

Consider $$Y_t =5+u_t-0.5u_{t-1}+0.25u_{t-2}$$ Because the regression has a constant (5) this is still valid? $$\rho_1=(θ_1+θ_1θ_2)/(1+θ_1^2+θ_2^2)$$
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21 views

What are the statistical properties of time delayed lagged time series?

Performing Taken's phase space delay embedding on the observations $\mathbf{z}$ of a univariate random variable, with an embedding dimension $d$, we get a realization of $n$ points such as: ...
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62 views

Does it make sense to compute adjusted $r^2$ with test set?

I have divided my time series into training and testing set. I would like to know if makes sense to compute the adjusted $r^2$ with the testing set or just on the training stage.
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22 views

Selecting optimal sample rate for time series prediction

Is there a procedure to choose the optimal sample rate (every second, minute, hour, ...) for time series prediction (say fitting an ARMA model)? I guess it depends on how many steps I want to predict ...
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1answer
30 views

Time series and random variable

I would like to know if the $n$ realizations of a variable, say $Y$ expressed in the form of a time series constitutes $n$ random variables or just a single random variable $Y$? For example, the ...
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33 views

On the Beta-t-EGARCH and the score

I am going to define the Beta-t-EGARCH model utilizing the more familiar GARCH model as does Harvey in Dynamic models for volatility and heavy tails (2008), I hope this will serve the purpose to ...
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12 views

Likert score significance testing between two surveys

I have two surveys taken one month apart. They contain 20 Likert-type questions (strongly agree, agree, neither agree or disagree, disagree, strongly disagree). I have added strongly agree and ...
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16 views

On the difference between parameter driven models and observation driven models

Could I have an explanation on what are parameter driven models and what are observation driven models as categorized by Cox (1981) in Statistical analysis of time series: some recent developments ...
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40 views

How to combine time series measured in multiple experiments?

I have recorded neural activity over time in mice while they perform a task. There are several mice, each ran different numbers of sessions, and repeated the task different numbers of times each ...
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The score of a dynamic model is a martingale difference sequence

I am going to write down some parts of Dynamic models for volatility and heavy tails by Andrew Harvey (2008) with my comments in bold and then ask for an alternative explanation of the final part. ...
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2answers
151 views

Fourier transform and the multivariate normal

I am wondering about how to specify multivariate normal distributions for vectors that have undergone a Fourier transform. For instance: Say we have the mean vector $\boldsymbol{\mu}$ and covariance ...
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69 views

Bootstrapping time series data: Circular block bootstrap

I have some very basic questions on circular block bootstrap applied to time series (dependent data). Let's suppose, I have a time series data like the one below. I know it's non stationary, but for ...
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63 views

Seasonal arima forecast equation

I need to compute a seasonal arima model, and make forecasts about vehicular traffic. My idea is to compute the model with R, and use the AR and MA coefficients in another application to predict ...
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1answer
47 views

Removing Seasonality

Excuse me for the basic question; however I am having trouble removing seasonality from this data. I have been using Win X-13 with no luck so far (it doesn't appear to do much to remove the ...
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153 views

How do I predict a time series with the help of other forecast time series?

If I have $n$ measured and interdependent time series $M_1, M_2, M_3..., M_n$ and have $n-1$ forecast time series $P_1, P_2, P_3..., P_{n-1}$, how can I predict the last forecast time series $P_n$? ...
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9 views

Which tool would be best analyzing human body movements and another persons reaction to it

Im wanting to look at specific movemnts of body parts over time and see if person A responds to person B in a certain way everytime/most of the time/some of the time person B does something specific.. ...
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1answer
43 views

Why doesn't the Moving Average model contain past time series values?

The moving average model looks like: $$X_t=\mu + \varepsilon_t + \theta_1 \varepsilon_{t−1} + \dotsb + \theta_q \varepsilon_{t−q}$$ It only contains the mean and some white noise factors, with lags. ...