Fractional integration analysis of precipitation dynamics: empirical insights from Nigeria

Figures & data

Fig. 1. Map of Nigeria. Source: pinterest.com.

Fig. 2. Rainfall data (mm) and estimated trends.

Table 1. Estimates of d (and 95% bands) in the model given by Eq. (1)(1) $${(1-B)}^d{x}_t=u_t, t=1,2,\dots ,$$(1) .

City	No deterministic terms (α = β = 0)	An intercept (β = 0)	A linear trend
Kano	0.25 (0.08, 0.44)	0.19 (0.05, 0.39)	0.19 (0.04, 0.39)
Kaduna	0.08 (0.02, 0.23)	0.11 (0.01, 0.27)	0.08 (−0.03, 0.24)
Ibadan	−0.05 (−0.12, 0.17)	−0.05 (−0.17, 0.13)	−0.05 (−0.17, 0.13)
Lagos	−0.02 (−0.08, 0.11)	−0.04 (−0.17, 0.16)	−0.10 (−0.25, 0.12)

The values in parenthesis refer to the 95% confidence interval of the non-rejection values of d. In bold, the selected model according to the deterministic terms.

Table 2. Estimated coefficients for the selected models in Table 1.

City	d (95% band)	Intercept	Time trend	Seasonality
Kano	0.19 (0.05, 0.39)	99.952 (3.86)	xxx	0.750
Kaduna	0.11 (0.01, 0.27)	101.091 (6.75)	xxx	0.827
Ibadan	−0.05 (−0.17, 0.13)	118.731 (18.81)	xxx	0.645
Lagos	−0.10 (−0.25, 0.12)	113.180 (8.89)	0.233 (1.72)	0.587

The values in parenthesis in the third and fourth columns are the corresponding t-values.

Table 3. Annual temperature, latitude and longitude of the studied regions.

City	Average Annual Temperature Range	Latitude/Longitude
Lagos	50 °F to 79 °F	6.5244°N/3.3792°E
Kano	53 °F to 102 °F	12.0022°N/ 8.5920°E
Ibadan	69 °F to 92 °F	7.3775°N/3.9470°E
Kaduna	55 °F to 95 °F	10.5105° N/7.4165°E

Source: (www.nimet.gov.ng).