To illustrate my points, I will assume that everybody has been asked whether they prefer Star Trek or Doctor Who and has to choose one of them (there is no neutral option). To keep things simple, let’...

For stationarity, the entire distribution of $p_t$ has to be constant over time, not only its mean. And while the mean of $p_t$ is indeed constant, e.g., it’s standard deviation isn’t. The larger $t$, ...

All simulation methods involve substituting random numbers into the function to find a range of values for the function. I have never heard of that definition of simulation. For example, Wikipedia’s ...

First of all, it is important to note that stationarity is a property of a process, not of a time series. You consider the ensemble of all time series generated by a process. If the statistical ...

TL;DR: You can’t. What is typically done The current “state of the art” in determining whether a network is a small world uses the following approach: Calculate the mean shortest path length $L$ ...

The curse of dimensionality is somewhat fuzzy in definition as it describes different but related things in different disciplines. The following illustrates machine learning’s curse of dimensionality: ...

The test statistics $p(k_2)$ is that of Fisher’s Exact Test. Since $$\sum_{k_2}^{n_2} \frac{1}{n_1+n_2+1}\binom{n_1}{k_1}\binom{n_2}{k_2}\binom{n_1+n_2}{k_1+k_2}^{-1} = \frac{1}{n_1+n_2+1},$$ ...

Usually you want to forecast the behaviour of a system to improve your reaction to and interaction with that system. But at the end of the day, forecasting is only a last resort, if it is not feasible ...

Consider the following examples: Your time series are the gross domestic products (GDP) of France and Germany. As the two country’s economics are strongly interacting, a strong French economy is ...

Different statistical tests answer different questions. The $t$ test comes in many flavours, but the most simple one answers the question whether the mean of a population is different from zero¹. The ...

You need to use the Fourier transform (and inverse transform) for real time series, i.e., rfft and irfft, respectively. This way you ensure that your surrogate is real. You can do this by replacing ...

What you need is a test that compares two distributions based on samples, such as the Kolmogorow–Smirnov test. In your case, you can compare the degree distribution of your original network to each ...

In most cases it depends on what exactly you mean by random, i.e., which null hypothesis you want to test. This again depends on your application, network acquisition, and underlying question. Two ...

I feel like classification is simply projecting the outcome of a certain data set onto a predefined group of outcomes, which sounds similar to forecasting. After all you may forecast ...

Is there any approximation theory in statistics that support this assumption (CLT?)? As already noted, white noise does not need to be normally distributed and I would assume that you find deviations ...

A non-linear time series is a time series which is generated by a non-linear process. For an regularly sampled time series $x_0, …, x_n$, this corresponds to a non-linear dependence of $x_t$ on $x_{t-... View answer Accepted answer 2 votes In an ideal world (for your purpose), the class mark is identical to the class’s mean, i.e.,$\$ x_i = \frac{1}{f_i}\sum_{j=1}^{f_i} y_{ij} = \frac{\sum\limits_{j=1}^{f_i} y_{ij}}{\sum\limits_{j=1}^{...

[…] de-trend and de-seasonalize a time series first so that it becomes stationary. First of all, this does not necessarily make the time series stationary. There are many other forms of ...

Showing that an observed time series is non-linear is notoriously difficult. Briefly, you would have to find a measure indicating nonlinearity (e.g., a positive Lyapunov exponent or a non-integer ...

If your time series has no autocorrelation, this indicates that the time information is irrelevant. To be on the safe side, you can confirm this using other methods such as the fourier transform or by ...

Does the varying window size (measured in points) adversely affect these statistics somehow? Strictly speaking, variance is a property of the distribution of your data points and all you can do is to ...

To evaluate the significance of the peak you have to formulate your a priori knowledge on the individual time series you are measuring as a null hypothesis. A likely null hypothesis would be that your ...

The difference between a stochastic process and a time series is somewhat like the difference between a cat on a keyboard and an answer on Stack Exchange: Cats on keyboards can produce answers, but ...

Regarding 1. and 2. It can very well be that other features of your time series (than you want to measure) lead to higher cross-correlations. To give an illustrative example (that does not exactly ...

Yes, if you look into the definitions, there will be obvious differences. I won’t do this here since there is no commonly agreed upon definition of local efficiency to begin with and what you write is ...

If I understand your data and setup correctly, you have what is called a bipartite graph (or bipartite network). This kind of network is defined by the following properties: There are two types of ...

You use Erdős–Rényi networks as instances of a null model for your real data. Thus the answer to your question depends on what null model is appropriate to your situation. Are disconnected networks ...

You seem to conflate the following two concepts typically denoted as frequency: The inverse of the period of a periodic signal or component. I refer to this as frequency in the following. The number ...