I want to fit a harmonic regression model to the Lotka-Volterra model

[HarithaJagadeesh]

I am trying o fit a harmonic regression to the training data of prey population, predict it in the test data and find the RMSE value so that I can compare it with the other fits ( like smoothing spline) and determine which one is better. Inorder to do that, I tried using the lm() command but the prediction was coming in a very small range and I could not figure out why. So I tried making it a ts() object and fit it but then I was getting errors with the fourier command saying K must be not be greater than period/2 and Number of periods does not match number of orders.
Can anyone help me with this?

This is the data :
`library(ggplot2)
require(mvtnorm)
library(KGode)

noise= 0.1 ## set the variance of noise
SEED = 19537
set.seed(SEED)
#Define ode function, we use lotka-volterra model in this example.
#we have two ode states x[1], x[2] and four ode parameters alpha, beta,
#gamma and delta.
LV_fun = function(t,x,par_ode){
alpha=par_ode[1]
beta=par_ode[2]
gamma=par_ode[3]
delta=par_ode[4]
as.matrix( c( alphax[1]-betax[2]x[1] , -gammax[2]+delta*x[1]*x[2] ) )
}
#create an ode class object
kkk0 = ode$new(2,fun=LV_fun)

#set the initial values for each state at time zero.
xinit = as.matrix(c(0.5,1))
tinterv = c(0,120)
#solve the ode numerically using alpha=1, beta=1, gamma=4, delta=1.
kkk0$solve_ode(c(1,1,4,1),xinit,tinterv)
#Add noise to the numerical solution of the ode model and
#treat it as the noisy observation.
y_true= t(kkk0$y_ode)
n_o = max( dim( y_true) )
t_no = kkk0$t #time points for each observation
y_no = y_true + rmvnorm(n_o,c(0,0),noise*diag(2))
#splitting to training and test set

set.seed(123)
data = data.frame(t_no,y_no)
train_prop =0.8
train_index <- createDataPartition(1:nrow(data), p = train_prop, list = FALSE)

#Split the data into training and test sets
train_data <- data[train_index, ]
test_data <- data[-train_index, ]

#Separate the prey and predator populations in the training set
train_data_prey <- train_data[, c(1, 2)]
train_data_predator <- train_data[, c(1, 3)]

#Separate the prey and predator populations in the test set
test_data_prey <- test_data[, c(1, 2)]
test_data_predator <- test_data[, c(1, 3)]
This is the harmonic model I tried but the prediction were not coming out wellharmonic_model <- lm(X2 ~ sin((2pit_no)/6) + cos((2pit_no)/6), data = train_data_predator)
summary(harmonic_model)
#Predict using the Harmonic Regression Model
test_data_predator$predicted <- predict.lm(harmonic_model, newdata = test_data_predator, type = "response")`

Can someone please help me?
Thanks,
Haritha

[robjhyndman]

This is not the place to ask for help. Please post your question at http://crossvalidated.com or at https://community.rstudio.com/