Quantitative Methods

Question 1

Accuracy

Answer 1

What was my accuracy with actually all
(TP+TN)/(TP+FP+TN+FN)

Question 2

Bias error

Answer 2

Degree to which model fits training data. Algorithms erroneous assumptions produce high bias with poor approximation
Causes underfitting and high in-sample error

Question 3

Breusch-Godfrey

Answer 3

Used for positive serial correlation. More general than DW

Question 4

Breusch-Pagan

Answer 4

One tailed test
Used for conditional heteoskedasticity. Null hypothesis of homoskedasticity. Tested by regressing the squared residuals against the original independent variables.
Test statistic is n x R_squared_residuals.
Under null hypothesis follows a chi-squared distribution
Correction: Use robust standard errors (e.g., White-corrected standard errors) or Generalized Least Squares (GLS).

Question 5

Covariance Stationary Conditions

Answer 5

Constant Mean: The expected value (mean) of the series is constant and finite for all periods: E(Y t ​ )=μ.
Constant Variance: The variance of the series is constant and finite for all periods: Var(Y t ​ )=E[(Y t ​ −μ) 2 ]=σ 2 .
Constant Autocovariance: The covariance between values at any two time periods depends only on the distance (lag) between the periods, not on the specific point in time: Cov(Y t ​ ,Y t−k ​ )=γ k ​ for any time t and lag k.

Question 6

Data Wrangling - Aggregation

Answer 6

Two or more variables combined into one

Question 7

Data Wrangling - Conversion

Answer 7

Converting variables into appropriate type for analysis

Question 8

Data Wrangling - Extraction

Answer 8

New variable created from existing one e.g. data of birth -> age

Question 9

Data Wrangling - Filtration

Answer 9

Data rows not needed must be identified and filtered (e.g. row with entry for non-US state)

Question 10

Data Wrangling - Selection

Answer 10

Data columns not needed must be removed (e.g. Name)

Question 11

Test for unit root to test whether data is covariance non-stationary

Answer 11

Check if: 1) Expected value is constant and finite. 2) Variance is constant and finite. 3) Covariance with itself for a fixed lag is constant and finite. Use the Dickey-Fuller test.
Dickey-Fuller test for unit roots could be used to test whether the data is covariance non-stationarity. The Durbin-Watson test is used for detecting serial correlation in the residuals of trend models but cannot be used in AR models. A t-test is used to test for residual autocorrelation in AR models.

Question 12

Document Frequency

Answer 12

Sentence count with word / Total number of sentences

Question 13

Dummy variable misspecification

Answer 13

If we use too many dummy variables (e.g. >n-1), there will be multicollinearity

Question 14

Duplication error

Answer 14

When there are duplicates of the data

Question 15

Durbin-Watson

Answer 15

Test for serial correlation in residuals of trend models but cannot be used in AR models. tests if
ϵ_t =ρϵ_t−1+u_t.
DW = ~2(1-ρ), where ρ is the sample correlation between residuals from one period to another
D=2 no serial correlation
D<2 positive serial corerlation (usually around 4)
D>2 negative serial correlation (usually around 0)
If its between upper and lower limit inconclusive
Above upper limit fail to reject
Below upper limit reject

Question 16

F-statistic

Answer 16

MSR/MSE
Assumes all slope coefficients simultaneously 0
Rejection if F>F(critical)

Question 17

F-statistic joint hypothesis

Answer 17

((SSE_R - SSE_U)/q) / (SSE_U/(n-k-1))
q is number of excluded variables in restricted model

Question 18

F1 score

Answer 18

(2 × P × R) / (P + R)
Harmonic mean of precision and recall

Question 19

FPR

Answer 19

FP/(TN+FP)

Question 20

How are qualitative independent variables incorporated into regression models?

Answer 20

Using dummy variables (binary 0 or 1 variables). To distinguish between n classes, use n-1 dummy variables.

Question 21

How can a time series with a unit root be transformed for analysis?

Answer 21

By first differencing: modeling the change in the variable (Yt​−Yt−1​) instead of the level.

Question 22

How can overfitting be addressed?

Answer 22

Use validation samples, cross-validation (like K-fold), penalized regression (like LASSO), reducing model complexity, or using ensemble methods (like Random Forests).

Question 23

How does Hierarchical clustering work?

Answer 23

Builds a hierarchy of clusters. Agglomerative (bottom-up) starts with individual points and merges clusters; Divisive (top-down) starts with one cluster and splits them.

Question 24

How does K-Means clustering work?

Answer 24

Partitions data into ‘k’ clusters by iteratively assigning observations to the nearest centroid and recalculating centroids until assignments stabilize.

Question 25

How is model performance evaluated in classification?

Answer 25

Using metrics like Accuracy, Precision, Recall, F1-score, ROC curve, and AUC derived from a confusion matrix (TP, FP, TN, FN)

Question 26

How is seasonality detected and corrected in time-series models?

Answer 26

Detected by testing for significant autocorrelation at seasonal lags. Corrected by adding a seasonal lag (another independent variable) to the AR model.

Question 27

How is the Regression Sum of Squares (RSS) calculated?

Answer 27

1. Subtract the mean from each predicted observation. 2. Square each result. 3. Sum the squared results. Degrees of freedom = k.

Question 28

How is the Sum of Squared Errors (SSE) calculated?

Answer 28

1. Subtract the predicted value from each observed value. 2. Square each result. 3. Sum the squared results. Degrees of freedom = n-k-1.

Question 29

How is the Total Sum of Squares (SST) calculated?

Answer 29

1. Subtract the mean from each individual observation. 2. Square each result. 3. Sum the squared results. Degrees of freedom = n-1.

Question 30

Impact of conditional heteroskedasticity (underestimate)

Answer 30

No effect on coefficient estimate Std Err of coefficient overestimated More type II

Question 31

Impact of serial correlation

Answer 31

No impact on coefficient estimate Std Err underestimated More type I error

Question 32

Inaccuracy Error

Answer 32

Where the data is not a measure of true value

Question 33

Incompleteness Error

Answer 33

Where data not present, resulting in missing data. Must be deleted or replaced with imputed data using mean, median, mode or assuming 0

Question 34

Inconsistency Error

Answer 34

Data conflicts with corresponding data points or reality

Question 35

Invalidity Error

Answer 35

Data outside of meaningful range, causing data to be invalid (e.g. date of birth in the future)

Question 36

K-fold Cross Validation

Answer 36

Data excluding test sample and fresh data shuffled randomly and divided into k equal subsamples K-1 samples in training set and kth used as a validation sample K typically between 5 or 10 Process repeated k times, which helps minimize both bias and variance by insuring each data point is ued in training set k-1 times and in validation set once

Question 37

LASSO

Answer 37

Least absolute shrinkage and selection operator Type of penalized regression, where penalty term has form lambda x sum(regression coefficients) In addition to minimizing the sum squared residuals, LASSO mnimises the sum of the absolute values of the regression coefficients Help to build more parsimonious models, is a regularizing method applied in asset management

Question 38

MSE Formula

Answer 38

SSE / (n-k-1)

Question 39

Name some supervised learning algorithms and their uses.

Answer 39

Penalized Regression (Regression, reduces overfitting), Support Vector Machine (SVM) (Classification), K-Nearest Neighbor (KNN) (Classification), CART (Classification/Regression), Random Forest (Classification/Regression, ensemble).

Question 40

Name some unsupervised learning algorithms and their uses.

Answer 40

Principal Components Analysis (PCA) (Dimension Reduction), K-Means Clustering (Clustering), Hierarchical Clustering (Clustering).

Question 41

Newey-West Standard Errors

Answer 41

Used to correct positive serial correlation

Question 42

Non-uniformity error

Answer 42

Data not present in identical format

Question 43

Normalised variable X

Answer 43

Xi-Xmin / Xmax - Xmin

Question 44

Precision

Answer 44

How precise are the predictions of positive TP/(TP+FP)

Question 45

Recall

Answer 45

Remembering all the actual positives. TP/(TP + FN)

Question 46

Standard error of autocorrelation

Answer 46

1/sqrt(T), where T is just the number of observations

Question 47

Standardised variable X

Answer 47

Xi - mu / sd

Question 48

Steps in structured data-based ML models

Answer 48

1) conceptualization of the modeling task, 2) data collection, 3) data preparation and wrangling, 4) data exploration, 5) model training.

Question 49

Steps in text-based ML models

Answer 49

1) text problem formulation 2) data (text) curation 3) text preparation and wrangling 4) text exploration 5) model training.

Question 50

Steps to determine appropriate autoregressive model

Answer 50

Add different lags until the serial correlation is removed, by testing the autocorrelation of the lags?

Question 51

Text cleansing

Answer 51

Remove HTML tags Remove punctuation, but preserve some context e.g. \end sentence\ instead of period Remove numbers replace with words 1->\one\ or \number\ to help reduce noise Remove excess whitespace

Question 52

TPR

Answer 52

TP/(TP+FN)

Question 53

Trimming

Answer 53

When extreme values removed (e.g. top 5% and bottom 5%)

Question 54

Variance error

Answer 54

Degree to which model's results change in response to new data from validation and test samples. Unstable models pick up noise and produce high variance causing overfitting and high out of sample error

Question 55

What are common text wrangling techniques?

Answer 55

Tokenization, removing stop words, lowercasing, stemming, lemmatization, creating Bag-of-Words or N-grams.

Question 56

What are the assumptions underlying a multiple linear regression model?

Answer 56

1. Linearity between dependent and independent variables. 2. No significant multicollinearity. 3. Expected error is 0. 4. Homoscedasticity (constant error variance). 5. No serial correlation (errors are independent). 6. Errors are normally distributed.

Question 57

What are the key steps in a data analysis project?

Answer 57

Conceptualize model, Collect data, Prepare & Wrangle data (cleanse, transform, scale), Explore data (EDA, feature selection/engineering), Train model, Evaluate model.

Question 58

What are the main types of machine learning?

Answer 58

Supervised learning (labeled data), Unsupervised learning (unlabeled data), Deep learning (neural networks with many layers), Reinforcement learning (agent learns through rewards/penalties).

Question 59

What are the principles of good model specification?

Answer 59

Grounded in economic reasoning, appropriate functional form, essential variables only, no violation of assumptions, tested out of sample.

Question 60

What do AIC and BIC represent, and how are they used?

Answer 60

Lower AIC (n×ln(SSE/n)+2(k+1)) or BIC (n×ln(SSE/n)+ln(n)(k+1)) indicates a better fitting model. They penalize adding variables, BIC more heavily. AIC is better for prediction, BIC for goodness of fit. difference in second part A = 2, B = ln(n) acho->A=2 B lyin -> B=ln(n)

Question 61

What happens to the coefficients of correlated independent variables when a new correlated variable is added to the model?

Answer 61

Adding the new variable will change the coefficient for the other correlated variables.

Question 62

What is a random walk process?

Answer 62

A time series where the predicted value in one period is equal to the value in the previous period (b1 = 1). Not covariance stationary. If b0 ≠ 0, it's a random walk with drift.

Question 63

What is a unit root, and how is it tested?

Answer 63

Occurs in an AR model when b1 = 1, leading to a non-stationary (random walk) process. Tested using the Dickey-Fuller test, which tests if (b1 −1)=0.

Question 64

What is Autoregressive Conditional Heteroskedasticity (ARCH)?

Answer 64

When the variance of the error term in one period depends on the variance in a previous period. Tested by regressing squared residuals on lagged squared residuals: ϵ^2t = a^0 + a^1 ϵ^2t−1 + μt.

Question 65

What is Conditional Heteroskedasticity and how does it affect statistical inference?

Answer 65

Error variance changes systematically with the independent variable. It can lead to underestimated standard errors (Type I errors) or overestimated standard errors (Type II errors). Detected using residual plots or Breusch-Pagan test. Corrected using White-corrected standard errors.

Question 66

What is Logistic Regression used for?

Answer 66

Used for qualitative dependent variables, modeling the probability of an event happening (between 0-1). The dependent variable is the log odds: ln(1−P/P).

Question 67

What is mean reversion in a time series?

Answer 67

A tendency for the series to move back towards its long-term average. Occurs in AR models when $\$

Question 68

What is Multicollinearity and how does it affect regression analysis?

Answer 68

Significant correlation exists between two or more independent variables. Causes unreliable coefficient estimates and inflated standard errors, leading to insignificant t-statistics (Type II errors). Detected by high pairwise correlations, insignificant t-tests with a significant F-test, or VIF > 10. VIF = 1 / (1-R^2) R^2 regression of independent variable on all the others Corrected by excluding problematic variables.

Question 69

What is overfitting in machine learning?

Answer 69

When a model learns the training data too well, including noise, resulting in poor performance on new, unseen data (high variance error). It often occurs with complex models or insufficient data.

Question 70

What is Serial Correlation and how does it affect statistical inference?

Answer 70

Error terms are not independently distributed. Positive serial correlation leads to underestimated standard errors and overestimated T/F statistics (Type I errors). Detected using residual plots, Durbin-Watson test, or Breusch-Godfrey test. Corrected using Newey-West standard errors.

Question 71

What is the purpose of Principal Component Analysis (PCA)?

Answer 71

To reduce dimensionality by summarizing correlated features into a smaller set of uncorrelated factors called principal components (eigenvectors).

Question 72

White-corrected standard errors

Answer 72

Used to correct for conditional heteroskedasticity

Question 73

Winsorisation

Answer 73

Values above a cutoff are replaced with highest/lowest non-outlier value