Optimizing Moving Average System

Hello

I am trying to optimize a moving average crossover system (LONG ONLY: For the sake of simplicity). The rules are simple: BUY when fast moving average crosses above(over) slow moving average. I have created an objective function as follows:

function SMA_CROSS_NAV = macrossnav(x,prices)
fastMA = x(1);
slowMA = x(2);
returns = tick2ret(prices);
MAFAST = movavg(prices,'simple',fastMA);
MASLOW = movavg(prices,'simple',slowMA);
signal = MAFAST > MASLOW;
strategy_returns = returns.*signal(1:end-1);
strategy_nav = ret2tick(strategy_returns);
SMA_CROSS_NAV = -(strategy_nav(end)-strategy_nav(1));
end

I am trying to find out that which set of FAST & SLOW moving average will maximize the SMA_CROSS_NAV value!

I have created the following script for the optimization process:

%% Step 1: Load the input data
load UNITYdata.mat
figure
plot(dateIS,closeIS)
grid on;
xlabel('Time (years)')
ylabel('Price')
title('UNITY FOODS LIMITED (PSX)')

%% Step 2: Set up the optimisation problem
warning off;

%% Define objective function
fH = @(x) macrossnav(x,closeIS);

%% Define design variables
% Design variables and initial guess
fastMA = 1:100;
slowMA = 101:200;
x0 = [fastMA;slowMA];

%% Define constraints
% Upper and lower bounds
lb = [1;100];
ub = [101;200];


% Linear inequalities (fastMA must be smaller than slowMA)
A = 1:200;
b = -1;

% Linear equalities
Aeq = [];
Beq = [];

%% Step 3: Perform the three optimisation techniques

%% Pattern search optimization
x_ps = patternsearch(fH,x0,A,b,Aeq,Beq,lb,ub)

%% Use the genetic algorithm optimisation
x_ga = ga(fH,numel(x0),A,b,Aeq,Beq,lb,ub)

%% Use the fmincon solver
opt = optimoptions('fmincon','Algorithm','interior-point','Display','off');
opt.TolFun = 1e-20;
opt.OptimalityTolerance = 1e-20;
opt.StepTolerance = 1e-20;
opt.FiniteDifferenceStepSize = 1;
x_f = fmincon(fH,x0,A,b,Aeq,Beq,lb,ub,[],opt)

Running the above script gives an error. I have attached the picture of the error.

Any help on how to correct the mistake and run the optimization process in a correct manner would be hugely appreciated.

I have attached the data file as well.

Thank you.

Regards,

Maisam

[Torsten]

You define an initial guess of 200 elements, but lower bounds and upper bounds have only 2 elements.

Further note that fmincon and ga will give non-integer values for the optimization parameters whereas movavg only works with positive integers as 3rd argument.

[Maisam Zaidi]

Alright!

What will be the best solution in order to find the best parameters for moving averages. How can I write the code correctly?

[Torsten]

The easiest way seems to be brute force: Call "macrossnav" for the possible integer combinations of x(1) and x(2) and take the combination for which you get back a minimum value for SMA_CROSS_NAV.

[Maisam Zaidi]

Alright. That seems possible.

I will do that.

Thank you.