Corrigendum to “Forecasting of Tilapia (Oreochromis niloticus) production in Bangladesh using ARIMA model”

Proposed correction:

2.2.1. Model identification

$${\mathrm{X}}_{\mathrm{t}}=\mathrm{\mu }+{\mathrm{\epsilon }}_{\mathrm{t}}+{\mathrm{\theta }}_1{\mathrm{\epsilon }}_{\mathrm{t}‐1}+{\mathrm{\theta }}_2{\mathrm{\epsilon }}_{\mathrm{t}‐2}+\dots +{\mathrm{\theta }}_{\mathrm{q}}{\mathrm{\epsilon }}_{\mathrm{t}‐\mathrm{q}}{\mathrm{X}}_{\mathrm{t}}=\mathrm{\mu }+{\mathrm{\epsilon }}_{\mathrm{t}}+{\mathrm{\theta }}_1{\mathrm{\epsilon }}_{\mathrm{t}‐1}+{\mathrm{\theta }}_2{\mathrm{\epsilon }}_{\mathrm{t}‐2}+\dots +{\mathrm{\theta }}_{\mathrm{q}}{\mathrm{\epsilon }}_{\mathrm{t}‐\mathrm{q}}$$ (1)

Here, X_t is the observed value at time t, μ is the mean of the time series, ε_t is the white noise error term at time t, and θ₁,θ₂, …,θ_qθ₁,θ₂, …,θ_q were the parameters to be estimated.

$${\mathrm{X}}_{\mathrm{t}}={\mathrm{\phi }}_1{\mathrm{X}}_{\mathrm{t}‐1}+{\mathrm{\phi }}_2{\mathrm{X}}_{\mathrm{t}‐2}+\dots +{\mathrm{\phi }}_{\mathrm{p}}{\mathrm{X}}_{\mathrm{t}‐\mathrm{p}}+{\mathrm{\epsilon }}_{\mathrm{t}}{\mathrm{X}}_{\mathrm{t}}={\mathrm{\phi }}_1{\mathrm{X}}_{\mathrm{t}‐1}+{\mathrm{\phi }}_2{\mathrm{X}}_{\mathrm{t}‐2}+\dots +{\mathrm{\phi }}_{\mathrm{p}}{\mathrm{X}}_{\mathrm{t}‐\mathrm{p}}+{\mathrm{\epsilon }}_{\mathrm{t}}$$ (2)

Here, X_t is the observed value at time t, φ₁,φ₂, …,φ_pφ₁,φ₂, …,φ_p are the autoregressive parameters, and ε_t is the white noise error term at time t.

2.2.2. Estimation of parameters

$$MAPE=\frac{100\%}{n}\sum _{t=1}^n\left|\frac{e_t}{y_t}\right|$$ (6)

where e_t is the error term, $y_t$ is the observation, and $\widetilde{y_t}$ is the forecast, and $e_t=y_t-\widetilde{y_t}$.

$$\text{BIC}={\mathrm{T}}^{\prime }\log \left({\mathrm{\sigma }}^2\right)+(p+q+1){\text{logT}}^{\prime }$$ (8)

Here, σ² denotes the mean square error and T′ indicates the number of observations used. The model with the lowest BIC value would be the best [28].