# Questions tagged [runs]

Runs refers to repeated occurrences of one outcome. For example, in repeated tosses of a coin, there will be runs of heads and tails. In the sequence HHHTHT there are 4 runs (one of length 3 and 3 of length 1).

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### LR test for overlapping return data using bootstrap

I wish to test a null hypothesis as in Christoffersen (1998) to see whether a sequence of Value-at-Risk forecasts $Q_t(p) \in \mathcal{F}_t$ possesses correct conditional coverage. Here $p \in [0,1]$ ...
0answers
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### Interpretation of Wald-Wolfowitz Runs Test for detecting Covariate Shift

I have been looking at several documents about applying statistical methods in R for detecting covariate shift in machine learning models. A few articles have recommended using the runs test for this ...
0answers
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### How to run test for randomness on a ternary cyclic sequence?

I would like to do a run test for randomness on a ternary sequence ($x_n \in \{0,1,2\}$) where a run is said to continue if the value increases by 1 cyclically (i.e. $(x_{n+1}-x_n)=1 \text{ mod } 3$). ...
1answer
30 views

### Probability of n successful runs [duplicate]

My background the past while has been project management so I haven't really had much work with stats the past decade or so, so please forgive the terminology if it is wrong. I'm working on a problem ...
0answers
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### What are the necessary steps required for conducting a Wolfowitz runs test of randomness, given that I have all the necessary data?

I am writing a part in my thesis about the random-walk theory of price changes. I plan to set up a runs test of randomness to show whether the price changes do follow a particular random pattern. I ...
2answers
230 views

### Is it normal to get more variance in k folds cross-validation of an algorithm than in k repetitions?

Is it normal to get a lot more variance in k folds cross-validation of an algorithm than in k repetitions of the same algorithm (neural network) on the same dataset? ...
0answers
66 views

### Deriving the average and variance of number of runs in runs test

NIST states that the average and variance of a number of runs in the "runs above and below median" test as  \overline{R} = \frac{2n_a n_b}{n_a + n_b} + 1 \\ s^2 = \frac{2n_a n_b(2n_a n_b - n_a - n_b)...
1answer
32 views

### How can I use the distribution of run lengths to test if a sequence is generated from flips of a fair coin?

I have a very long sequence (in the tens of thousands) of binary outcomes from some data-generating process. I believe that these outcomes are iid Bernoulli trials with p = 0.5, equivalent to flipping ...
1answer
44 views

### Including streaks/runs in (generalized) linear mixed model context

The data and model used so far: I have longitudinal count data on 16 pens (8 with treatment A, 8 with treatment B). Each pen houses the same number of animals, and the pens may be considered as ...
2answers
342 views

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### Upper and lower limits for numbers of runs

On this website about statistical process control there is a chart which gives the upper and lower limits for the number of runs in a set of data for the data set to be considered taken from a process ...
1answer
290 views

### Runs test for randomness for k elements

Say I have a sequence of length $n$ of $k$ different elements, s.t. $n > k, k > 2$. I want to show this sequence is random, based on the number of runs. I found this paper by AM Mood which ...
1answer
855 views

### Null hypothesis of the Wald-Wolfowitz runs test

From Wikipedia The runs test (also called Wald–Wolfowitz test after Abraham Wald and Jacob Wolfowitz) is a non-parametric statistical test that checks a randomness hypothesis for a two-valued data ...
0answers
129 views

### In general which runs test is more powerful?

There are several tests for randomness, one is runs up and down, another is run against mean or some other values, of cause, Bartel's rank test can also be used. There are studies shows where Bartel'...
1answer
645 views

### Runs Test and Chi Square Distribution

I want to identify random data by applying some tests to the observed byte stream. I used the chi square test already on a frequency analysis, which works fine. To reduce the false-positive rate I ...