Statistical Measures

T-Statistic

The t-statistic measures how far your sample result (like sharpe ratio or excess return) is from the null hypothesis in terms of standard error.

P-Value

The p-value represents the probability of observing a result at least as extreme as the one you got if the null hypothesis were true.

Concepts

shuffle

Weather the data is randomly shuffled before being split into training and test sets.

Skewness and Kurtosis

Under the influence of significant causes, the normal distribution can get distorted. The distortion can be calculated using skewness and kurtosis. Skewness refers to the degree of symmetry, or more precisely, the degree of lack of symmetry; Positively Skewed: the values are more concentrated towards the right side; Negatively Skewed: the data points are more concentrated towards the left side; Kurtosis refers to the proportion of data that is heavy-tailed or light-tailed in comparison witha normal distribution. Positive Kurtosis: light tailed Negative Kurtosis: heavy tailed, like punching the distribution;

zero skew: mean = median

correlation

Rule of Thumb

0.00–0.19: Very weak.

0.20–0.39: Weak.

0.40–0.59: Moderate.

0.60–0.79: Strong.

0.80–1.00: Very strong.

Data Leakage

Use scaler trained by train data to transform test data to avoid test set's mean and standard deviation would influence the scaling, "leaking" information from the test set into the preprocessing step .

zip()

the word zip means to fasten or join two things together quickly, like closing a zipper on a jacket. It aligns two rows of teeth into one unified strip.

R2

R-squared, evaluate the performance of a regression model. range from 0-1, R^2=1 - SS_res / SS_tot SS_res means sum of the squared redisuals (differnce between actual and predicted values) SS_tot means sum of squares (variance of the actual data from its mean)

Confusion Matrix

Classification metrics; A CM compares predicted discrete labels to actual discrete labels, counting how often predictions match or deviate from the truth.

Accuracy Score

The proportion of correct predictions out of all predictions.

Precision Score

The proportion of true positive predictions out of all positive predictions made by the model;

Recall Score

The proportion of true positives identified out of all actual positives;

Fl Score

The harmonic mean of precision and recall; F1 = 2 * (Precision * Recall) / (Precision + Recall) Harmonic mean is a type of average that's particularly useful when dealing with rates, ratios or quantities that are inversely related. HM empasizes smaller values. Harmonic is a balancing act. It doesn't let a model check bby excelling in one metric while failing in another. And sensitivity to weakness. Harmonic because it's derived from the reciprocals , and the reciprocal nature is what makes it sensitive to smaller values. Harmonic origins from Greek harmonikos meaning sklled in music or relating to harmony. Everyday sense: something harmonic suggests balance, agreement, or a pleasing arrangement, like in music where harmonics are tones that resonate together smoothly. Harmonic means working together in a balanced, reciprocal way.

ROC Curve

Receiver Operating Characteristic curve. Receiver refers to a signal receriver in early radar and communication systems. Operating how the receiver functions as you adjust its decision threshold; Characteristic the trade-off between detecting true signals(True Positive Rate) and false alarms (False Positive Rate); So, Receiver Operating Characteristic literally means the characteristic performance of a receiver in operation, reflecting its ability to distiniguish signal from noise across different settings. ROC Curve is a plot of TPR vs FPR as you adjust the decision threshold. Threshold means predict 1 only if prob > threshold; It's like a tuning knob for model;

Seasonal Decompose

Dickey-Fuller test

Developed in 1979. DF test tests the nul hypothesis that a unit root is present in an autogregressive (AR) time series model.

null hypothesis

Ho, is the claim in scientific research that the effect being studied doesn not exist. The H0 can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed. The null hypothesis and alternative hypothesis are types of conjectures used in statistical tests to make statistical inferences, whcih are formal methods of reaching conclusions and separating scientific claims from statistical noise.

alternative hypothesis

There is sufficient evidence supporting the credibility of alternative hypothesis.

Conjecture

A conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof.

ADF(Augmented Dickey Fuller)

ADF is a statistical test used to determine whether a time series is stationary or has a unit root. Stationary is a key assumption in many time series models, meaning that the statistical peoperties of the series (like mean and variacnce) do not change over time. THe presence of a unit root suggests that the series is non-stationary, often indicating a trend or random walk behavior.

A unit root refers to a characteristic of a time series where its statistical properties, like mean and variance, are not constant over time, making it non-stationary.