What is a timeseries
A time-series is a dataset collected over a timespan.
Stationarity/ White noise
In general, we need stationary time series in order to build statistical models. That means there should be no systematic change in the mean/variance of the data.Also, the data should have no seasonality (periodic fluctuations). However, most financial/economic data is non-stationary. That means there is some trend (systematic change) or seasonality.Therefore we need to transform this data in order to […]
Using t-value for two-sided hypothesis testing
Is your t-value bigger than your alpha half quantile? if yes then you can reject the null hypothesis. Eg. Your t-value is -1.954 while your alpha half quantile is (5%) and therefore -1.645 Therefore your t-value is bigger than your alpha half quantile and you can reject the null hypothesis.
p-value
Shows you the probability that you are wrong in case you reject the null hypothesis. (cause it is actually right) Example 1: Eg. You have a p-value of 4%. That means if you reject the null hypothesis you will make a mistake with a probability of 4%. Example 2: Eg. You have a p-value of 40% That means if you […]
Linear Regression
By doing a regression try to explain a (dependent) variable by means of a linear function through another (independent) variable. These two variables have a correlation (that is more or less than 0) Below you see a scatter plot that indicates a correlation between variables X and Y. X could be the returns of the Sample EM Index and Y […]
Correlation
You have a set of data points. Make sure it’s normally distributed -> (eg. Take log returns). Then you measure the correlation of the data points. Place the data points on a scatter plot (as you can see below). The scatter plot shows us the distribution of data. EXAMPLE: Let’s say on the x axis is the amount of job […]
Capital growth rate
If you want to measure the increase of your capital over time, you can calculate the difference between the initial value and the current value. Example: Let’s say you made an investment in a stock one year ago. Its price was 100 Euro. Today, one year later, the price is: 110 Euro Now calculate the capital growth rate: Formula: Todays […]
The value of money at different times
IIf you buy a bond, you become a lender to the bond issuer. In return for lending money, you, in many cases, receive interest payments. Against this background, one should remember that the interest payments one gets closer to today are more valuable than those one receives in the distant future. E.g., if you get one euro tomorrow, it is […]
Is a distribution left or right skewed?
Quck analysis: If a data distribution is skewed the data is not distributed symetricaly. An example that is often used to show left skewnes is the salary distribution in most capitalist countries. There are some high earners which account for a higher mean then median Eg lets asume in a country there are 5 people which have the following incomes […]
T-Test (one sample)
The t-test shows if your expected mean assumption is reasonable or not. With a t-test you try to answer the following question: How likely is your mean estimate (eg. 1,36%), if the mean of the total population would be..% (eg.1,5%) -> in other words is your sample mean close enough to the total popultion mean that you can assume for […]