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The Fourier transform decomposes a signal (a function of time) into frequencies, giving the energy at each frequency.

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How to fit a model to both daily and weekly periodic data using linear regression and fourier transform

I have a variable, y, in 30 minute intervals, and is highly dependent both on the time of day and the day of the week - mainly Sundays. It is also dependent on bank holidays, which could by any day of ...
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13 views

Characterizing periodicity level of signal after two-dimensional Fourier transform

I have a sequence of vectors, each of them is an 88-dimensional vector. For example, [0, 0, 0, 1, 0,....]. I want to measure whether this sequence has periodicity, and I have used 2-dimensional ...
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29 views

Forecasting seasonality with Fourier terms in R

I am using the auto.arima from the forecast package in R to determine the optimal K-terms for fourier series. After I do that, ...
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1answer
19 views

R forecast multiple seasonality optimal model search using fourier and msts objects

Hi I have hourly data (one obs one hour) with multiple seasonality. I would like to fit an ARIMA model using forecast R package taking into account the multiple seasonality, maybe taking also in ...
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119 views

Time Series Analysis: Fourier Transform [closed]

I've recently studied Fourier transform and I've applied it on a time series data, since I am still confused between time and frequency domain I doubt the authenticity of my code to calculate Fourier ...
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36 views

Fourier Output Meaning

I just ran a fourier series on weekly sales data for 3 years worth of data. I optimally chose the number of k-terms based on the AIC. First 6 lines of my data: ...
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18 views

Is there a concept of weakly periodic in stats? If so, what is it called?

Ok, say we have a signal that reoccurs within every T+x time where T is a constant and x is a random number small in size compared to T. We know that a function is actually periodic if F(x) = F(x+T), ...
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21 views

How to generate synthetic data with specific spatiotemporal correlation

My dataset represents a field evolving over time, so has dimensions [X,Y,T]. I would like to generate synthetic data with the same autocorrelation structure and spatial correlations as the real data (...
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40 views

Need help understanding output of a periodogram

In my effort to understand the output of a periodogram I created a series (s) where 1,1,1,1,1,1,1,1,1,10 is repeated 100 times and then created a periodogram of this series using the following R code: ...
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1answer
139 views

Discrete Fourier transform of an exponential decay

I have a vector with an exponential decay signal, using Numpy: t=np.arange(128) a=0.1 decay=np.exp(-a*t) I would like to compute the discrete Fourier transform (...
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1answer
432 views

Forecasting with ARIMA ( Training and Test Data split)

I have an hourly time series of the average parking occupancy with data available from September 2017 up until June 2018. I would like to use the ARIMA model with external regressors to produce a ...
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113 views

Fourier transform of a Gaussian process

I would like to discuss and ask a question regarding the Fourier transform of a Gaussian process, if it makes sense. For that purpose, let me describe the following situation. Let $z(s)$ be a ...
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47 views

Sampling from characteristic/moment generating function

Suppose I am given a probability distribution only via its characteristic or moment generating function and I want to sample from that distribution to generate paths in a Monte Carlo simulation. Is ...
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19 views

Finding common trends in time-series

I have a 10 relatively noisy time-series. I want to check if there are any similar trends in the 10 sets. My simple way of initially looking would just be to cross-correlate each time-series with ...
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59 views

Applications of FFT algorithm in statistics? [duplicate]

Are there any applications of the FFT algorithm in basic statistics i.e.: estimating a density distribution? I would like to learn more about it - and it would be nice to work on an actual example ...
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16 views

Fourier Transform based imputation

Fourier Transform based imputation Can any body please assist me in understanding the Fourier Transform based imputation algorithm shown in Figure. I am struggling to understand ts and te. Link of ...
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13 views

How does the variance of a simulated Gaussian random field scale with the number of terms in the Fourier decomposition?

I numerically simulated a Gaussian random field and am trying to verify that the program is working correctly. One way is to check the variance of the result vs. the theoretical prediction. However I'...
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22 views

Linear regression on circulant matrices

I am reading the paper on High-Speed Tracking with Kernelized Correlation Filters and I am a bit stuck on the equivalence of Ridge regression in the frequency domain. Minimizing the typical equation ...
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83 views

How to interpret the Output of the following ARIMA model

How to interpret the output of the below ARIMA(with Fourier Terms) code y <- msts(ts(dataAR$Total[57:331]), seasonal.periods=c(30.4375,91.3125)) Model ...
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36 views

Time series/ ARMA Simulation

Given: I have a question, given a continuous real spectral density f(w), -infinity my idea: I would folding, discretize and truncate the spectral density to get a real (one-sided) discrete spectral ...
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0answers
24 views

Standardization of cyclical features for Clustering

I am about to start a project in data mining sales data using the well-known algorithm, t-SNE. Specifically, I have 4 millions of observations and 75 attributes for every sale. A graphical example ...
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107 views

FFT machine learning model for different rotation speeds

I am working on a machine learning model, that can classify different failure patterns of a rotating machine / motor based on a supervised approach. My features for the model are based on the ...
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1answer
125 views

Calculating right values of Periodogram using Fourier Analysis

In the book, Economic Cycles: There Law and Cause By Henry Ludwell Moore, he plots Periodogram of rainfall of Ohio valley. He uses 72 years data (1839-1910) and tries to find the most dominant cycle ...
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1answer
307 views

tbats() model not capturing seasonality (weekly data)

I have below 4 years of weekly data which has complex seasonality of varying seasonal length. 1) My first question is what should be the correct assigned frequency for this series (frequency() comes ...
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23 views

Full frequency space description of a continuous-time random process (e.g. signal) in

I don't know if signal processing or math would be a better forum, but I'll start here. Consider an ensemble of stationary random processes $x(t)$ that has the following properties: The PDF is $P[x]$...
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1answer
311 views

Proof of Herglotz Theorem in Time Series Analysis

I am studying time series, following Time Series Theory and Methods by Brockwell and Davis. I am reading the proof of the Herglotz Theorem, I have the following questions. First, the proof given in ...
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119 views

Kernel density estimation with FFT for a univariate non-parametric regression

The non-parametric regression model to be estimated looks like the following x_t = b(x_t-1) + epsilon_t Forfinding the optimal bandwith h in the kernel ...
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1answer
65 views

Spectral density and Riemann Stieltjes Integral

I am confused with a part about spectral densities. I found it in Time Series Theory and Methods by Brockwell and Davis. I don´t understand how is applied the Riemann Stieltjes Integral in this ...
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2answers
99 views

Is this a well-studied problem? Problem: Optimally unlagging multiple time-series

Is the problem of optimally lagging/unlagging multiple time-series with integer lags to maximize a sum of pairs of cross correlations or coherence an already well-studied problem? If so, references? ...
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33 views

Model Specification with dlmModTrig

I'm trying to figure out how to fit a dlm model to highly seasonal data (traffic counts per hour). The final goal is to determine the effect of a policy intervention that happened at time point x. My ...
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2answers
124 views

Power spectral density of the output of a linear time invariant system with a weakly-stationary process

Please note that I have no background whatsoever in Fourier analysis and very little in time series. This is exercise 2.10 in Theodoridis' Machine Learning: Show that the autocorrelation of the ...
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3answers
1k views

Spectral Analysis in R - the periodogram

I am doing a spectral analysis in R using the spec.pgram() function. Suppose I have observations for $y_1$ to $y_n$ which are a time series with annual observations....
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25 views

How to interpret uncertainties in interpolated and smoothed timeseries?

I have a years worth of surface reflectance data, collected daily via satellite. However, some days are totally cloudy, so there were no observations. That being said, I use linear interpolation to ...
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241 views

Why are random Fourier features non-negative?

Random Fourier features provide approximations to kernel functions. They're used for various kernel methods, like SVMs and Gaussian processes. Today, I tried using the TensorFlow implementation and ...
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1answer
37 views

Generating time series for electricity demand

I'm working on a project, trying to model electricity consumption and generation from a bunch of PV generators to see how much of the demand can be satisfied by the production in the "town". Most ...
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200 views

How to define a loss function for discrete fourier series?

In each batch there are 8000 sample points, and I apply discrete Fourier transform on them. The original samples are real valued, so only the half of the result is needed. The end result is 4000 ...
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31 views

Representation of Noise in Fourier transform

I perform an experiment where I sample $M(k)$ which is in theory related to $|f(x)|^2$ via $M(k)=\int e^{ikx}|f(x)|^2\,dx$. I perform the discrete FT on my data in order to obtain $|f(x)|^2$. Without ...
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2answers
874 views

Dealing with multi seasonality in time series

I am new in R and time series analysis and need some help. I am currently trying to create a tool to forecast the demand of power for a company. On my data set I have 17550 observations that ...
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1answer
559 views

Finding out frequency of peaks using the Fourier transform

I have a signal that varies in time as shown below. I have just shown a 5 s interval of data (from 97 s to 102 s). The sampling frequency is 1000 Hz. My goal is to find out the frequency of the ...
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35 views

Comparing power in FFT frequencies biased by number of bins?

I have some EEG data recorded from a mouse with tremor. When I do an FFT on the data, it generally looks like an exponential distribution. I'm interested in any frequency peaks that are ...
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How to measure a mean frequence of fft transform

I have this time series (utilization of app by day of an user) And this fourier transform of the above time series How can I extract one number that express the mean frequency of this time series? ...
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61 views

Regression for Analysing Fourier Transform of a Complex Function

Regression for Analysing Fourier Transform of a Complex Function I need to analyse a linear system which is y = FT{x}, where Input x and output y are both complex function (A*exp(jθ)). If I only ...
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187 views

FFT as feature for neural network

i am trying to make a classifier that determines whether the audio sample provided is a girl or a boy. however i am only getting 50% accuracy on my classifer at the moment. I want to know if its the ...
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1answer
156 views

Energy savings prediction model using stochastic processes and Monte Carlo Simulation

I want to build a model that quantifies the energy savings from a building retrofit project. For example a company is using a heating oil radiator system, that is meant to be replaced by a gas ...
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0answers
129 views

detecting change point in the time series on a 2 dimensional space

I have a 2 dimensional geographic space. There are crime events occuring at different regions in the space over time. I am looking particularly at property crimes like burglary. If I look at the time ...
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435 views

Get the amplitude of the components of a periodic signal from Fourier (FFT)/Wavelets analysis

I have a signal looking approximatively as the one in the first subplot below (*), and I would like to: extract the periods of the main components of the signal; associate an amplitude to these ...
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3answers
1k views

What information can I gain from the fourier transform?

I have acceleration data in 3D vectors (x,y,z). For detecting certain patterns within the ...
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0answers
118 views

Deseasonalizing a time series using a Wiener-Kolmogorov filter

I am trying to eliminate seasonality from a time series using Wiener-Kolmogorov filter, I am following the methodology explained in here this paper about signal extraction which is the same followed ...
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1answer
1k views

Deseasonalizing data with fourier analysis using MATLAB [closed]

I am trying to eliminate seasonality from my data using Fourier analysis in MATLAB. Following this post https://stackoverflow.com/questions/19285684/fast-fourier-transform-for-deasonalizing-data-in-...
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1answer
190 views

How to compute bernoulli distribution PDF from CF

The characteristic function for a Bernoulli distribution is $$\phi(t) = (q+pe^{it}) \text{ where } p+q=1$$ I also know that the relationship between $\phi(t)$ and the pdf $f(k)$ is the Fourier ...