# Tagged Questions

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### Problem defining ARIMA order

This is a long post so I hope you can bear with me, and please correct me where I'm wrong. My goal is to produce a daily forecast based on 3 or 4 weeks of historical data. The data is 15 minute ...
293 views

### Fourier/trigonometric interpolation

Background In a paper from Epstein (1991): On obtaining daily climatological values from monthly means, the formulation and an algorithm for calculating Fourier interpolation for periodical and ...
133 views

### Power Spectral Density (PSD) relation to Time domain

I calculate the Power Spectral Density of a time series, X, using the Lomb-Scargle periodogram. I am trying to reconstruct the amplitude of X from the Lomb-Scargle periodogram. I have read that due to ...
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### Spectrogram and the coefficient of variation

As I understand it, after applying the Fourier transform we get a graph, where on the X-axis marked the frequency (or wavelength) and on the Y-axis amplitude (or decibels). But sometimes there are ...
100 views

### Given samples from multiple normal RVs, how do we recover the histogram of their means?

Let $X_1,...,X_N$ be independent normal random variables. $X_i$ is normal with mean $\mu_i$ and standard deviation $\sigma_i$. Let $x_i$ be a single random sample from $X_i$. Input: We get all ...
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### Discrete Fourier Transform and uneven sampling

In this blog article an example is given of one can use the DFT to detect frequencies much higher than the sample rate. In the comments sections I asked how it was done, since DFT normally requires ...
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### Can the proof of the central limit theorem be expressed as the limit of a convolution with an operator

The central limit theorem, as I understand it (engineer, non-statistician), says that the distribution comprised of means of some other reasonably behaved distributions converges to a normal ...
150 views

### Unevenly sampled data and the Lomb-Scargle method

I managed to estimate the periodogram of unevenly sampled data using the Lomb-Scargle Method. Analyzing the frequency domain it would be interesting to filter out a frequency band and then apply IFFT ...
145 views

### Characteristic function and Fourier transform

I understand the definition of characteristic functions used in probability theory: For a random Variable $X$ with probability density function $f_X$ the characteristic function is defined as: ...
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### Deconvolution with fourier transform or characteristic function?

Let us consider the following model: $$Y_j = X_j + \epsilon_j \hspace{15pt} j=1, ..., n$$ Where $Y_j$ is a noisy signal, $\epsilon_j$ is the noise which is independend from the signal $X_j$. We have ...
117 views

### Separating two complex-valued datasets that have been multiplied together

I have two complex-valued datasets, A and B that can be considered as vectors with the same number of elements. The datasets are multiplied together using complex point-by-point multiplication, ...
326 views

### How to test statistical significance of coherence coefficients in spectral analysis?

I would be very thankful for advising me how to test statistical significance of coherence coefficients. I have a statistical software that calculates them for me but it does not test their ...
318 views

### “Central limit theorem” for weighted sum of correlated random variables

I'm reading a paper which claims that $$\hat{X}_k=\frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}X_je^{-i2\pi kj/N},$$ (i.e. the Discrete Fourier Transform, DFT) by the C.L.T. tends to a (complex) gaussian random ...
482 views

### Similarity of two discrete fourier tranforms?

In climate modelling, you're looking for a models that can adequately portray the Earth's climate. This includes showing patterns that are semi-cyclical: things like the El Nino Southern Oscillation. ...
188 views

### Finding the instantaneous period of a signal (or calculating period degradation)

I have a signal, of varying amplitude, and after a certain point in time, I expect to see the period of this signal lengthen. I am looking for a way to measure the lengthening of this period. Is this ...
198 views

### P-value approximation from an underlying unknown distribution

I am calculating a certain statistic(relative entropy) of a certain sequence alignment over DNA sequences. The statistic has a certain distribution in the entire genome of which I only have 1000 ...
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### Clustering the elliptic Fourier series coefficients

What do you think about the best way to perform a search for two discrete group membership in data that consist of four Fourier series coefficients like this: ...
229 views

### How can one do “two series” Fourier analyses in R?

In Statistica one can do a "two series"/bivariate/cross spectrum Fourier analysis to examine the coherency, gain, and phase spectrum across a pair of signals. It is probably a failing on my part, but ...
660 views

### Analysing periodicity in sparse time series

I am interested in looking for periodicities in a several day long recording of electrical activity. The traces present a very steady baseline over which, from time to time, some short events (300-500 ...
890 views

### Fitting the parameters of a stable distribution

I have a data set and I have to fit this data set with a stable distribution. The problem is that the stable distributions are known analytically only in the form of the characteristic function ...
460 views

### Fourier transform of distributions

Which distributions are their own Fourier transform besides the normal distribution and the generalized arcsine distribution?
474 views

### How can I estimate the phase difference between two periodic time-series?

I have 2 daily time-series, each 6 years long. While noisy, they are both clearly periodic (with a frequency of ~1 year), but appear to be out of phase. I would like to estimate the phase difference ...
235 views

### Do I use non-normalized or normalized fft output from R to compute phase angle?

Is R's fft() output normalized or not? In other words, do I have to normalize the output first before computing the phase angle using ...
490 views

### Are real and imaginary components of frequency element of fft correlated?

I want to use model-based clustering to classify 1,225 time series (24 periods each). I have decomposed these time series using the fast Fourier transform and selected the harmonics that explain at ...
258 views

### STFT statistical analysis

I am using the evolfft function in the RSEIS R package to do a STFT analysis of a signal. The signal is one hour long and it ...