How to compare ARMA model with simple average moving in matlab

% Load data

data = readtable('sample data.xlsx');

Y = data.AdjClose;

% Split data into training and testing sets

train_Y = Y(1:2519);

test_Y = Y(2520:end);

%check if test_Y is empty

if isempty(test_Y);

test_Y= 0.001*ones(size(train_Y));

end

% Fit ARMA model to training set

p = 1;

q = 1;

Mdl = arma(p, 0, q, 'Constant', 'off');

EstMdl = estimate(Mdl, train_Y);

% Make predictions on testing set

forecast_horizon = ceil(length(test_Y) + 30); % Adjust forecast horizon according to test set length

y0=train_Y(end-p-q+1:end);%Set the initial condition

num_periods=30;%Number of periods to forecast

y_pred = predict(Mdl,test_Y,num_periods,'Y0',y0,'InitialCondition','z');

% Calculate trading signals based on ARMA model predictions

signal_arma = zeros(size(test_Y));

for i = 2:length(signal_arma)

if y_pred(i-length(test_Y)) > y_pred(i-1)

signal_arma(i) = 1; % Buy signal

elseif y_pred(i-length(train_Y)) < y_pred(i-1)

signal_arma(i) = -1; % Sell signal

end

end

% Calculate trading signals based on moving average

window = 20;

signal_ma = zeros(size(test_Y));

for i = window+1:length(signal_ma)

if mean(test_Y(i-window+1:i)) > mean(test_Y(i-window:i-1))

signal_ma(i) = 1; % Buy signal

elseif mean(test_Y(i-window+1:i)) < mean(test_Y(i-window:i-1))

signal_ma(i) = -1; % Sell signal

end

end

% Evaluate trading rule performances

returns_arma = signal_arma .* (test_Y - y_pred(end-length(test_Y)+1:end)); % Adjust the index to match the length of test_Y

returns_ma = signal_ma .* (test_Y - mean(test_Y));

cumulative_returns_arma = cumsum(returns_arma);

cumulative_returns_ma = cumsum(returns_ma);

% Plot cumulative returns

plot(cumulative_returns_arma);

hold on;

plot(cumulative_returns_ma);

legend('ARMA', 'Moving average');

% Calculate performance metrics

sharpe_arma = sqrt(252) * mean(returns_arma) / std(returns_arma);

sharpe_ma = sqrt(252) * mean(returns_ma) / std(returns_ma);

max_drawdown_arma = maxdrawdown(cumulative_returns_arma);

max_drawdown_ma = maxdrawdown(cumulative_returns_ma);

% Display performance metrics

fprintf('ARMA model:\n');

fprintf('Sharpe ratio: %.2f\n', sharpe_arma);

fprintf('Max drawdown: %.2f%%\n', max_drawdown_arma*100);

fprintf('\n');

fprintf('Moving average:\n');

fprintf('Sharpe ratio: %.2f\n', sharpe_ma);

fprintf('Max drawdown: %.2f%%\n', max_drawdown_ma*100);

Answer 1

[Nithin]

Hi @Martin Njagi,

In the code provided, the trading signal was not properly lagged, so the signal at time "t" was being applied to the return at time "t", effectively using future information. This can result in artificially inflated strategy performance, resulting in unreallisticaly high "Sharpe ratios". Modify the code such that the signal generated at time "t" is used to trade the return from "t+1".

signal_arma = [0; signal_arma(1:end-1)];
signal_ma = [0; signal_ma(1:end-1)];
strategy_ret_arma = signal_arma .* test_ret;
strategy_ret_ma = signal_ma .* test_ret;

Additionally, the calculation of maximum drawdown was performed on the cumulative log returns rather than on a realistic equity curve based on simple returns. Since log returns can accumulate to negative values, this method allowed the drawdown to exceed "100%", which is not meaningful in a trading context, no strategy can lose more than all of the invested capital.

ret = [0; diff(log(Y))]; % log returns
cumret_arma = cumsum(strategy_ret_arma); % cumulative log return

Refer to the results attached below after applying the updated approach on a sample dataset along with an unpdated Max Drawdown Calculation:

Kindly refer to the attached MATLAB code for better understanding.

Here's the corresponding MathWorks documentations for more information:

• arima: https://www.mathworks.com/help/econ/arima.html
• estimate: https://www.mathworks.com/help/econ/arima.estimate.html
• movmean: https://www.mathworks.com/help/matlab/ref/movmean.html
• Cumulative Product: https://www.mathworks.com/help/matlab/ref/double.cumprod.html