`notes :`

python packages to perform regression

in statsmodels.api as sm sm.OLS(y,x).fit()
in numpy np.polyfit(x , y , deg=1)
in pandas pd.ols ( y , x )
in scipy from scipy import stats stats.linregress(x,y)

`POINTS :`

correlation=sqrt(Rsquare)
Autocorrelation is corr of a single time series with a lagged copy of itself
with financial time series when returns have a negative autocorrelation it is mean reverting for vice versa condition trend following
plot_acf is statsmodels function for plotting the autocorrelation function

input x is a series or array lags = how many lags of the autocorrelation function will be plotted alpha sets width of confidence interval

to_datetime() is used to convert an index often read in as a string into a datetime index

df,index = pd.to_datetime(df.index)

changing an index to datetime

joining two dateframes

df1.join(df2)

computing percent changes and differences of a time series

df['col'].pct_change() df['col'].diff()

pandas correlation method of series

df['abc'].corr(df['xyz'])

correlation coefficient is ameasure of how much two series vary together

The positive correlation

means that when interest rates go down, stock prices go down. For example, during crises like 9/11, investors sold stocks and moved their money to less risky bonds (this is sometimes referred to as a 'flight to quality'). During these periods, stocks drop and interest rates drop as well. Of course, there are times when the opposite relationship holds too.

A first step when analyzing a time series is to visualize the data with a plot.

Autoregressive integrated moving average model (ARIMA)

An Arima model is a class of statistical models for analyzing and forecasting time series data.

AR: Autoregression. A model that uses the dependent relationship between an observation and some number of lagged observations.

I: Integrated. The use of differencing of raw observations (e.g. subtracting an observation from an observation at the previous time step) in order to make the time series stationary.

MA: Moving Average. A model that uses the dependency between an observation and a residual error from a moving average model applied to lagged observations.

The parameters of the ARIMA model are defined as follows:

p: The number of lag observations included in the model, also called the lag order.
d: The number of times that the raw observations are differenced, also called the degree of differencing.
q: The size of the moving average window, also called the order of moving average.

somiljain7 / time-series-analysis