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

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Test for autocorrelation

I wanted to test if there's significant autocorrelation in my data. Here's the reproducible code(R!) and the result. It looks like that dwtest and bgtest and acf are all too much different. Can ...
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Does the density of daily data impact forecast accuracy?

I know it might be trivial but does the density of daily values impact the forecast accuracy? For example, if a call center receives less than 50 calls for weekdays and less than 10 calls for weekend, ...
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9 views

mixed results for stationarity tests and structural breaks

Following situation: I want to forecast a time series of the number of trucks on the motorway in some country. Here how the regular week looks like: I have data for 4 years and divide the huge time ...
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13 views

Correlation on ordered subset

Imagine a hypothetical scenario in which a ball is thrown along a straight line. During flight, the position is continually sampled; however, at some distance, the sampling fails and only noise is ...
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31 views

Multiple regression model

I have a multiple regression equation which as four quarters (maybe called them as parameters) ...
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16 views

“Iterating”? For MA and AR processes

I am not sure what is being done here, but I keep seeing statements like Given $X_t - \phi X_{t-1} = Z_t$ $...(1)$ then $$X_t = -\phi^{-1}Z_{t+1} + \phi^{-1}X_{t+1}$$ $$ = ... $$ $$= ...
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Statistical test: Does actual time series data deviate from forecast?

I have made a prediction of future sales based on an ARIMA model. The ARIMA model is based on past data, during which there has been no marketing activity. During the period predicted by ARIMA, I will ...
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29 views

“Frequency” value for seconds/minutes intervals data in R

I'm using R(3.1.1), and ARIMA models for forecasting. I would like to know what should be the "frequency" parameter, which is assigned in the ts() function, if im ...
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9 views

Finding ACVF and two random variables

let $X_t = 0.5X_{t-1} + Z_t$ where $Z_t$ ~ $ WN(0,\sigma^2)$ I want to find the ACVF of both $X_t$ and $Z_t$, but I am a little bit confused. Say for $X_t$ $$\gamma(h) = Cov(0.5X_{t-1} + Z_t, ...
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1answer
17 views

How to construct appropriately reverting geometric AR(1) process?

Suppose I have a mean-reverting AR(1) type process, $X_{t+1} = X_t + \theta(\mu - X_t) + \epsilon_t$ where $\theta > 0 $ and $\mathrm{Var}(\epsilon_t) = \sigma^2$. This process is clearly ...
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29 views

Determine the causes of change in time with mixed models

I have a database with several continuous variables measured in two times. I searched for a change in time in my dependent variables in this way: ...
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22 views

Organizing data using time series multivariate regression?

I am trying to understand how I can organize the following data since none of what I learned in my undergrad econometrics course works. I am running out of ideas. I am trying to measure how the ...
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standardization within time series and across groups (nested data)

I read through the previous threads concerning standardization of variables, but unfortunately have not found an answer whether it is justifiable or necessary to z-standardize values across groups ...
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1answer
34 views

Stochastic Volatility Model

In Kim et al. (1998) stochastic volatility model is specified as: $y_t=\beta\exp({\frac{h_t}{2}})\varepsilon_t,\quad t\geqslant1$ $h_{t+1}=\mu+\phi(h_t-\mu)+\sigma_\eta\eta_t$ $h_1\sim ...
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42 views

How to implement a simple Bayesian Network for Time Series Data?

I'm a computer science grad student, with not much knowledge in Bayesian statistics, so I'm seeking for guidance for the simplest start. I have 10 variables, like demand, price etc. and I want to ...
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25 views

What is the source of nonstationarity in this VAR model?

I am trying to forecast a VAR model, which consists out of 5 variables with a monthly frequency. The problem is that the VAR model produces an unstable forecast and I am not sure what the source of ...
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1answer
18 views

Calculation of Higher-Order Cross-moments

How can I calculate standardized central cross-moments for 2 time-series? The 4th-order standardized central moment, kurtosis, is; ...
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30 views

Reverse engineer a predictive model from a time series graph

I have found some real estate plots in a scientific article. These graphs mainly describe, the believes of the author of the development of the real estate market in the future for certain countries. ...
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1answer
47 views

Outlier Detection in Time-Series: How to reduce false positives?

I'm trying to automate outlier detection in time-series and I used a modification of the solution proposed by Rob Hyndman here. Say, I measure daily visits to a website from various countries. For ...
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How to merge overlapping discontinued data time series?

I have two datasets consisting of the US Federal debt held by Federal banks with a timespan covering the period 1953Q1 to 1988Q4 and 1970Q1 to 2014Q2. (series FDHBFRB and FDHBFRBN from the FRED ...
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29 views

STL-decomposition of a time series with deterministic trend and seasonality

what is the relationship between STL-decomposition and deterministic components of time series like trend or seasonality? I have a time series with deterministic trend and deterministic seasonality, ...
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19 views

Unit root in shares

Suppose that dependent variable is a share of sth (for example it is a % of positive answers to the same question in each period of time t). If data shows the unit ...
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3answers
113 views

How do I detrend time series?

How do I detrend time series? Is it ok to just take first difference and run a Dickey Fuller test, and if it is stationary we are good? I also found online that I can detrend the time series by ...
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1answer
19 views

Matching two power signals for similarity

Below are the images of two signals that i plotted. Both the signals are from fridge belonging to different houses. Visually looking at the plot i can tell that these plots belong to fridge as they ...
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21 views

Longitudinal data: baseline effect versus random intercept 2

My question follows this post: Longitudinal data: baseline effect versus random intercept The topic is very interesting and I have two further questions, one very practical and another about ...
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20 views

Cross correlation of two power signals

I have two devices and their power usage data. I am trying to see how co related these two devices are. i.e If i use device 1 then how often i am using device 2. It will be helpful if anyone can ...
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31 views

PCA on spatial precipitation data time series

I have precipitation time series data stored in a 3D matrix called 'pre' (dim1/2=position (index), dim3=time). I want to do a principal component analysis in order to detect the main variance and thus ...
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Extract ocasional peak and recent trend from noisy time series with threshold driven sampling of an impulse signal

I have event sampled time data for several measurements for a large number of units. The data is recorded only when the measurement is above a threshold. The measurement amplitude increases, and then ...
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63 views

ARIMAX with a specified nonlinear model using the arima function in R

I am interested in fitting an ARIMAX model using R. As known, ARIMAX can be understood as a composition of ARIMA models and regression models with exogenous (independent) variables. I have a time ...
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21 views

How to improve linear model generalization when autocorrelation is present?

I have features $X_t$ and response $Y_t$ (all continuous variables) and my objective is to find the best estimate of $f(X_t)=Y_t$ where $f$ is linear, and 'best' is defined as lowest generalisation ...
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2answers
56 views

What's the minimum sample size required to do a time series analysis?

I'd like to know the minimum number of monthly data points required to do time series analysis with the seasonality effect in forecasting. I read some articles & they were saying that 50 or 60 ...
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44 views
+50

Predicting Y from a regression model for dY

I have some time series data where I'm modelling temperature as a function of various predictors. On physical grounds, I can expect that $$\frac{dT}{dt} \propto T_a - T$$ where $T_a$ is the ambient ...
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47 views

Time series with autoregressive error

How can I in R fit a time series, $x_t$, with external regressors, $v_t$, and an autoregressive error? This time series model is given as follows, $x_t = \beta v_t + \epsilon_t$ where $\epsilon_t = ...
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Multivariate Time Series Forecasting in R - data in 10 minute intervals

I have data where an observation was made in 10 minute intervals for 8 weeks. I have around 170 variables that were measured every 10 minutes. I am trying to use multivariate time series analysis to ...
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What does a linear/geometric probability in time series mean?

In some discrete time series I analyzed I'd like to interpret whether there is a meaning to the observed probability model. The data is some discrete time series with a population of objects which at ...
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1answer
71 views

stationarity in time series

I'm learning a Time series course and I have a few questions. Strictly stationary is a process if the joint distribution of $X_{t1},X_{t2},...,X_{tm}$is the same as the joint distribution of ...
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7 views

How to fit a series into another one so that their mutual information is minimized?

I am building a multivariate model of an output series. I have many series-candidates for inputs. I want to select the inputs based on the mutual information between these inputs and the output. My ...
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21 views

Glue time series back together

I have a long time series whose distribution I don't know. I take snapshot of a fix window at random places of the time series to get a set of equal length shorter time series. Now without the help of ...
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23 views

Do we fit this time series data with time series model or spline?

Basically, I have the following data with the number of item A on the vertical axis and the time on the horizontal axis (from 1st hour to the 24th hour). I don't have much experience in fitting a ...
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27 views

Time series and ACD model

When we say fractional gaussian noise is subordinated to Autoregressive Conditional Duration model, what does it mean (explanation using equation will be great)?
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1answer
38 views

Analysis of irregularly sampled time series

What is the difference between irregularly sampled time series and non-linear time series? Also, what are the best methods for the analysis of irregularly sampled time series? Are there any sample ...
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1answer
47 views

How to build a function with the result of auto.arima in R?

I use: fit = auto.arima(Y, xreg=X) in R to get ARIMA(1,0,0), result as follows: ...
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wrong x axis label for time series plot of daily data [migrated]

I have 4 years of historical daily data. I plotted time series with command plot() and put xaxt="n" to customize the x axis. If ...
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1answer
61 views

Counterintuitive result when comparing two groups of time series

I have two groups of time series and I am testing the hypothesis that the groups can be distinguished in some way. Each time series is measurements of an individual’s pupil size as they listen to an ...
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1answer
55 views

Understanding $O_p$

One thing I feel like I have never mastered is the concept of $O_p$ convergence and how to use it. I understand the basic idea and what bounded in probability means, but I always have a hard time ...
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46 views

Filtering of time series

I would like information (references) about the reason why time series should be filtered before being used in a VAR model. Thank you in advance, Nikos.
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34 views

Autocovariance of an AR(3) process

I am given a general equation of an AR(3) process : $Y_t\:=\:e_t\:+\:\Phi _1\:Y_{t-1}+\:\Phi _2Y_{t-2}\:\:+\:\Phi _3Y_{t-3}$ I want to find the $\gamma _0$ of the AR(3) process but I am not too sure ...
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cointegration analysis for different level stationary series

I have a data set of of three variables: imports, exports and GDP. The import variable is I(1), but the export variable is I(1) only for constant and constant and trend but not for none. Similarly, ...
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what is 1-step ahead prediction for this AR(2) model?

AR(2) model : rt= 1.2rt-1 - 0.35 rt-2 +at, Var(at)=16 Suppose that r300 = 7, r299=5, and r298=6 What is the 1-step ahead prediction of r301 at the forecast origin T=300? Compute the variance of ...
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How much training data is enough for seasonal time series forecast

I am new to times series forecast. If I have data(single variable and timestamp) with double seasonality periods, which are 288 and 1056. And I use tbats in R to build time series data and then ...