Spyder 1st order autocorrelation

As an AI language model, I don't have the ability to run Spyder or any other software. However, I can explain what first-order autocorrelation is and how it is calculated.

Autocorrelation is a statistical technique used to measure the degree of similarity between a time series and a lagged version of itself. A first-order autocorrelation measures the correlation between a variable and its immediately preceding value.

To calculate the first-order autocorrelation, you can use the following formula:

r1 = (sum((xi - x_mean) * (xi+1 - x_mean)) / (n - 1)) / (sum((xi - x_mean)^2) / (n - 1))

where r1 is the first-order autocorrelation coefficient, xi is the ith observation, x_mean is the mean of the series, and n is the number of observations.

The resulting value of r1 will range between -1 and 1, with a value of 0 indicating no autocorrelation, a positive value indicating positive autocorrelation (i.e., the variable tends to be high when it was high in the previous period), and a negative value indicating negative autocorrelation (i.e., the variable tends to be low when it was high in the previous period).