The stakes extend far beyond academic bragging rights. Livestock herding in Somalia contributes about 45 percent of national GDP and more than 80 percent of foreign currency earnings, largely through exports to the Gulf States. Yet the sector is battered by recurrent droughts, transboundary animal disease outbreaks, and sudden import bans from destination markets. When shocks strike, their effects do not fade quickly; herd rebuilding takes years, and the losses ripple through national meat output for a decade or more. Accurate forecasting is therefore not a luxury but a foundation for food security planning in one of the world’s most climate-vulnerable states.

The research team, led by Abdirisak Osman Bade, drew on the Food and Agriculture Organization’s FAOSTAT database, filtering the raw records to include only the four pillars of the pastoral economy: camels, cattle, sheep, and goats. Commercial poultry was deliberately excluded because it plays almost no role in Somalia’s rangeland-based production system. After cleaning, the dataset yielded a continuous series of 64 annual observations from 1961 to 2024, with mean production of 144,214 metric tons per year and a standard deviation of roughly 40,269 tons. The distribution was nearly symmetric, with a skewness of just −0.15, but its flat kurtosis of −1.52 hinted at the long stretches of stable output punctuated by crisis-driven collapses that define the country’s pastoral history.

Before any model could be trusted, the team had to establish the statistical character of the series. Augmented Dickey-Fuller and Phillips-Perron unit-root tests both failed to reject nonstationarity in the raw data, with p-values of 0.544 and 0.424 respectively. After first differencing, however, both tests rejected the null decisively at p < 0.001, confirming that production is integrated of order one, or I(1). A Zivot-Andrews test allowing for structural breaks in both intercept and trend returned a statistic of −4.3992 and pinpointed a breakpoint around the year 2000, reinforcing the picture of a series shaped by regime shifts rather than smooth evolution.

Seven forecasting frameworks then competed on a blind out-of-sample test covering 2015 to 2024, having been trained on data from 1961 to 2014. The contenders included the classical ARIMA and Theta models, the state-space approaches ETS, BATS, and TBATS, the fractionally integrated ARFIMA model, and an autoregressive neural network. The ARFIMA model, which permits fractional differencing and thereby captures hyperbolically decaying autocorrelations, dominated every accuracy metric. It achieved a symmetric mean absolute percentage error of just 3.11 percent, a root mean squared error of 10,836.89 tons, a mean absolute scaled error of 0.85, and a Theil’s U statistic of 0.69, well below the 1.0 threshold that marks superiority over a naive random walk.

The neural network came second, with an sMAPE of 4.49 percent and an RMSE of 12,825.75, confirming that machine learning can capture nonlinear patterns but cannot match long-memory econometrics when the historical record is short and volatile. The classical and state-space models fared far worse. ARIMA posted an sMAPE of 11.41 percent, while ETS reached 12.20 percent, and BATS and TBATS produced identical errors because Somalia’s annual data contains no seasonality for the trigonometric components of TBATS to exploit. The authors attribute these failures to systematic bias: short-memory models produce overly smoothed trajectories that completely miss real-world shocks, assuming that disturbances either decay rapidly or persist indefinitely, when in fact drought impacts linger for years at intermediate strength.

Rolling-origin cross-validation reinforced the ranking. Using an expanding-window procedure that repeatedly re-estimated each model across sequential training partitions, the ARFIMA model posted an aggregate RMSE of 10,595.91 against 11,900.06 for the neural network, demonstrating that its dominance was not an artifact of one particular test decade. The biological explanation lies in the slow recovery of herd demographics. The 2016/17 drought alone caused an estimated deficit of 14.8 million animal births, including 10.5 million among goats and 4 million among sheep, alongside 4 million excess deaths. Such reproductive gaps translate into multi-year production lags that only fractional integration can represent mathematically.

The species-level breakdown reveals a striking ecological asymmetry. Camel meat production rose steadily across the full 64-year horizon, barely dipping during droughts, a testament to the species’ ability to maintain milk and meat offtake under extreme water scarcity. Cattle production, by contrast, collapsed dramatically during the 1991 civil conflict and the multi-season drought of 2022, while goats and sheep remained comparatively stable, with goats showing the stronger post-drought recovery. Local surveys of drought-stricken districts in southwest Somalia report herd losses of up to 62.1 percent for goats, 68.6 percent for cattle, 74.7 percent for sheep, and 63.5 percent for camels, figures that align closely with the contraction the models now project.

Fitted to the full historical record, the ARFIMA model projects a slow, steady decline in national red meat output through 2034, falling from 175,332.80 tons in 2025 to 168,884.30 tons by 2034. Confidence bands widen with the forecast horizon, stretching from roughly 113,000 to nearly 225,000 tons at the 95 percent level by the end of the decade. The authors interpret this projected plateau as evidence that Somalia’s traditional pastoral system may be approaching its dynamic ecological and structural limits, as chronic pasture depletion, reduced biomass regeneration, and compounding droughts constrain the demographic expansion of herds toward a new equilibrium.

The findings carry a pointed message for policymakers and donors. The study argues that transitioning from reactive, crisis-driven aid to proactive climate resilience requires targeted investment in digital index-based livestock insurance, commercial fodder value chains, and mobile veterinary infrastructure, all anchored to mathematically validated baselines of the kind the ARFIMA model now provides. The authors also acknowledge limitations: the univariate design cannot incorporate climate covariates such as vegetation indices or rainfall anomalies, the small sample restricted the neural network’s architectural depth, and FAOSTAT’s national aggregations inevitably blend informal cross-border trade and unrecorded subsistence slaughter into the official figures. Future work, they suggest, should integrate high-resolution spatial and climatic data within hybrid architectures. For now, the lesson is clear: in fragile dryland economies, the memory of past shocks is long, and only models that remember can see what is coming.

Subject of Research: Comparative time-series forecasting of pastoralist red meat production in Somalia using classical, state-space, long-memory, and neural network models

Article Title: Forecasting pastoralist red meat production trajectories in a fragile and climate-vulnerable state: a comparative evaluation of classical, state-space, long-memory, and neural network models in Somalia

Article References: Bade, A. O., Shire, D. M., Hassan, S. M., & Muse, A. H. (2026). Forecasting pastoralist red meat production trajectories in a fragile and climate-vulnerable state: a comparative evaluation of classical, state-space, long-memory, and neural network models in Somalia. Pastoralism: Research, Policy and Practice, 16, Article 17161. https://doi.org/10.3389/past.2026.17161

Image Credits: AI Generated

DOI: 10.3389/past.2026.17161

Keywords: Somalia, pastoralism, livestock forecasting, ARFIMA, long memory, neural networks, ARIMA, climate vulnerability, food security, drought, time series analysis, FAOSTAT

The team, led by Luis A. Gil-Alana of the University of Navarra in Spain together with OlaOluwa S. Yaya of the University of Ibadan in Nigeria, Ramiro Gil-Serrate of Universidad Antonio de Nebrija and Peter O. Ohue of Queens University, set out to answer a deceptively simple question: when a wet or dry month arrives in these drylands, how long does its influence persist? The answer matters enormously for the hundreds of millions of people whose agriculture, livestock and water supplies depend almost entirely on rain-fed systems. If rainfall shocks fade quickly, droughts are transient annoyances; if they persist, a single bad season can cascade into years of hardship.

To quantify persistence, the researchers turned to the econometric concept of fractional integration. In classical time-series analysis, a series is either stationary, meaning shocks die out quickly, or nonstationary, meaning shocks accumulate indefinitely and require full differencing to stabilise. Fractional models allow an intermediate possibility: a differencing parameter d that can take any real value. When d lies between zero and 0.5, the series displays long memory, with autocorrelations that decay hyperbolically slowly rather than exponentially fast, so disturbances echo through the record for a very long time even though the series ultimately reverts to its mean. When d reaches or exceeds 0.5, the series becomes nonstationary and shocks become effectively permanent in statistical terms.

The innovation in this study lies in extending that framework to seasonality. Monthly rainfall is dominated by an annual cycle, and standard seasonal unit root tests such as the HEGY procedure assume that the seasonal pattern can be removed by differencing the data twelve months apart. Preliminary HEGY tests on the African data rejected both non-seasonal and seasonal unit roots, but the authors argue that such tests are too restrictive: forcing d to equal exactly one risks overdifferencing, which can manufacture spurious conclusions. Their seasonal fractional model instead treats the operator (1 minus L to the twelfth power) raised to the power d, where L is the lag operator and d is estimated freely from the data. This allows the seasonal memory of rainfall to be measured on a continuum rather than forced into a binary stationary-or-not verdict.

The data came from the Climatic Research Unit Time Series dataset hosted on the World Bank Climate Change Knowledge Portal, a globally gridded observational product built by interpolating station measurements onto a regular 0.5-degree grid. Each country series contained 1,488 monthly observations. The descriptive statistics alone tell a story of extremes: mean monthly rainfall ranges from a mere 1.8 millimetres in Egypt and 3.4 millimetres in Libya to more than 70 millimetres in Ethiopia and 83 millimetres in South Sudan. Coefficients of variation frequently exceed 100 percent in countries such as Niger, Mauritania and Namibia, and every series is positively skewed, reflecting long stretches of near-zero rainfall punctuated by occasional torrential events.

The headline finding is that all estimated fractional parameters fall strictly between zero and one, confirming genuine fractional integration in every country examined. But the values split the continent into two hydroclimatic camps. In one group, the estimates are low enough to guarantee stationarity: Somalia records the lowest value at 0.25, followed by Algeria, Tunisia and Kenya at 0.27, Morocco and Egypt at 0.32, and Botswana, Libya, South Africa and Namibia in the 0.36 to 0.40 range. In these countries, rainfall deviations from the long-term mean are corrected relatively quickly, and the confidence intervals rule out nonstationarity. At the other extreme, Mauritania (0.54), Niger (0.56), Sudan and South Sudan (0.60), Chad (0.66) and Mali (0.67) all show estimates at or above the 0.5 threshold, meaning rainfall anomalies there are highly enduring and revert only slowly. Ethiopia sits almost exactly on the boundary at 0.49.

The geography of these results is not accidental. The high-persistence countries are concentrated in the Sahelian belt, where rainfall arrives in a single monsoonal wet season governed by the annual migration of the Intertropical Convergence Zone and the West African Monsoon. Rainfall events in these regions occur in coherent seasonal sequences, and prolonged dry seasons with relatively low intra-seasonal variability enhance temporal persistence. By contrast, the low-persistence countries experience climatically noisy regimes. Kenya and Somalia are shaped by two distinct rainy seasons, the so-called long rains and short rains, modulated strongly by the El Niño-Southern Oscillation and the Indian Ocean Dipole, while Algeria and Tunisia receive episodic precipitation from Mediterranean cyclones and mid-latitude weather systems. Multiple, interacting rainfall-generating mechanisms fragment the seasonal signal and weaken long memory.

The study also detected statistically significant positive time trends in 10 of the 17 countries, with the steepest increases in Ethiopia and Kenya, equivalent to roughly 0.20 and 0.34 millimetres per year respectively under the white-noise specification. To check robustness, the authors repeated the analysis allowing for weakly dependent errors using the non-parametric Bloomfield approach, which approximates the spectrum of autoregressive moving average processes with far fewer parameters, and by aggregating the monthly data to quarterly series. The broad picture held: under the Bloomfield specification, stationarity was confirmed in the same ten countries plus Ethiopia, with only South Sudan, Chad and Mali remaining nonstationary, while the quarterly analysis pushed estimates slightly higher, leaving nine countries in the nonstationary camp, with Chad reaching 0.89 and Mali 0.84. Across all specifications, six countries, Somalia, Algeria, Kenya, Tunisia, Egypt and Morocco, showed consistent evidence of stationary rainfall.

For drought managers and agricultural planners, the implications are stark. In Mali, Chad and South Sudan, a drought year is not simply a bad year that the climate forgets; the statistical signature suggests its effects linger, compounding food insecurity and water stress over successive seasons. Conversely, in the Mediterranean-influenced north and the dual-season east, rainfall anomalies wash out faster, but the very variability that produces this rapid mean reversion also makes rainfall harder to forecast from one season to the next. The authors note that countries with higher seasonal persistence may require fundamentally different drought-monitoring and agricultural-planning strategies than those where anomalies revert quickly, and the findings underscore sharply differing levels of hydroclimatic resilience across the continent.

The authors are candid about limitations. Country-level averages can mask enormous sub-national diversity, particularly in climatically heterogeneous nations such as Kenya, Ethiopia, South Africa and Sudan, where distinct regional rainfall regimes coexist within national borders. Future work, they suggest, will examine monthly rainfall totals, anomalies relative to the 1991 to 2020 climate baseline, standardised precipitation indices and log-transformed series, as well as non-linear trends built from Chebyshev polynomials, Fourier functions or neural networks, and the possible role of structural breaks in creating spurious long memory. Even with these caveats, the study delivers a rare century-scale, statistically rigorous portrait of rainfall behaviour in some of the world’s most vulnerable drylands, and it offers a quantitative foundation for anticipating which regions will recover from climate shocks and which will carry them forward.

Subject of Research: Seasonal persistence and long-memory dynamics of rainfall in arid and semi-arid African climatic zones

Article Title: Testing seasonal persistence of rainfall in arid and semi-arid african climatic zones using a seasonal fractional model

Article References: Gil-Alana, L. A., Yaya, O. S., Gil-Serrate, R., & Ohue, P. O. (2026). Testing seasonal persistence of rainfall in arid and semi-arid african climatic zones using a seasonal fractional model. Theoretical and Applied Climatology, 157(10), Article 628. https://doi.org/10.1007/s00704-026-06551-x

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06551-x

Keywords: rainfall persistence, fractional integration, long memory, Sahel, drought, arid climates, seasonality, Africa, time series analysis, HEGY test, Intertropical Convergence Zone, hydroclimatology

The team, led by Manuel Monge of Universidad Francisco de Vitoria and Universidad Europea de Valencia in Spain, together with Jorge Aracil Jordá of Universidad Pontificia de Comillas and Juan Infante of Universidad Villanueva, set out to resolve a long-standing ambiguity in applied economics. Although consumer expectations and price levels are among the most intensively tracked macroeconomic indicators in the world, the applied literature offers a bewildering range of descriptions of their time-series behavior. Different studies classify the same series as stationary, trending, or unit-root processes depending on the tests used and the sample chosen, leaving policymakers without a clear picture of how lasting an economic shock to confidence or purchasing power really is.

To cut through that ambiguity, the authors adopted what they describe as a unitary empirical strategy rather than a conventional multivariate one. Each series was examined on its own terms, with inflation and general consumer confidence indicators maintained as context series. The first step was a rigorous classification of the order of integration of each variable using augmented versions of the Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin procedures, two of the workhorse tools of time-series econometrics. By explicitly accounting for deterministic specifications such as intercepts and trends, these tests determine whether a series must be differenced once to become stable, or whether it already fluctuates around a fixed mean.

The results of that first stage were clear. The Index of Consumer Sentiment, the purchasing power of the consumer dollar, and the broader consumer confidence index all emerged as first-order integrated, meaning they are non-stationary in levels and only settle down after being differenced. Inflation, by contrast, proved to be level stationary, fluctuating around a stable long-run value without requiring differencing. The purchasing power series itself was constructed as the inverse of the Consumer Price Index for all items for urban consumers, so it directly measures how much real consumption a dollar can command at any point in time.

But the study did not stop at the binary distinction between stationary and non-stationary. The authors then estimated a fractional differencing parameter for each series, allowing the order of persistence to lie along a continuum rather than forcing each variable into one of two rigid categories. This fractional integration framework, which has gained traction in macroeconomics over recent decades, captures the idea that many economic processes are neither quickly mean-reverting nor permanently drifting, but something in between: they remember shocks for a very long time, with the effect of any disturbance decaying only slowly, often over years or decades.

The fractional estimates delivered the study’s most intriguing finding. For consumer sentiment, purchasing power, and consumer confidence, the estimated differencing parameters clustered slightly below or slightly above one, placing all three processes in the non-stationary region of the continuum while still implying a capacity for slow recovery toward their means. In practical terms, this means that a collapse in consumer confidence or an erosion of real purchasing power is not necessarily permanent: the series can, in principle, drift back toward their historical average levels, but only gradually, with the imprint of the shock visible in the data for a long time. The consumer price index itself, meanwhile, was not easily differentiated from a unit root, indicating that price levels behave as though shocks to them accumulate without a reliable tendency to reverse.

Perhaps the most counterintuitive result concerns purchasing power. Among the mean-reverting series in the study, purchasing power turned out to be the most mean-reverting of all, a finding the authors note runs contrary to most expectations, which hold that mean-reverting data should exhibit the longest memory. The implication is that the real value of the consumer dollar, despite being buffeted by oil shocks, financial crises, pandemic-era supply disruptions, and the sharp inflation surge of 2021 through 2023, retains a stronger tendency to return toward its long-run level than sentiment or confidence measures do. Each series was specifically characterized through the results, giving economists a persistence fingerprint for every variable examined.

The authors are careful to draw a boundary around what their findings do and do not mean. The study finds no relationship between the estimated sentiment levels and affordability conditions, nor does it assert one. In other words, the statistical memory properties of consumer sentiment and the memory properties of purchasing power are characterized separately, and the paper does not claim that one drives the other or that the degree of persistence in feelings about the economy can be read off from the degree of persistence in prices. That restraint matters, because the temptation to link confidence and affordability causally is strong in both public debate and policy discussions.

Even so, the findings carry real weight for how economists and policymakers interpret the American economic mood. If consumer sentiment behaves as a highly persistent, near-unit-root process, then campaigns or interventions designed to restore confidence after a downturn should not expect rapid normalization; the psychological scar of a recession may persist for years, shaping spending and investment decisions long after objective conditions improve. Conversely, the comparatively stronger mean reversion in purchasing power suggests that the erosion of real wages and savings, while painful, has historically tended to correct itself over time as inflation subsides and nominal incomes adjust, a pattern visible in the data following the inflationary episodes of the early 1980s and the post-pandemic period.

The study also demonstrates the value of fractional integration methods for macroeconomic monitoring more broadly. Traditional unit-root tests force a stark either-or choice that can mislead: a series with a differencing parameter of 0.95 and one with a parameter of 1.05 may both fail standard stationarity tests, yet their long-run behavior differs meaningfully, with the former eventually reverting and the latter drifting without bound. By estimating the differencing parameter directly and reporting it along a continuum, the Spanish research team has provided a more nuanced map of persistence in some of the most consequential numbers in American economic life, from the confidence consumers express in surveys each month to the quiet, cumulative erosion and recovery of the dollar in their pockets. As debates over inflation, affordability, and economic anxiety continue to dominate headlines, the message of this research is that both prices and perceptions move on long timescales, and understanding their memory may be essential to anticipating when, and whether, they will return to normal.

Subject of Research: Long memory and fractional integration in US consumer sentiment and purchasing power, 1978 to 2025

Article Title: Long memory in consumer sentiment and consumer dollar purchasing power in the United States from 1978 to 2025

Article References: Monge, M., Jordá, J. A., & Infante, J. (2026). Long memory in consumer sentiment and consumer dollar purchasing power in the United States from 1978 to 2025. Discover Sustainability. https://doi.org/10.1007/s43621-026-04367-3

Image Credits: AI Generated

DOI: 10.1007/s43621-026-04367-3

Keywords: consumer sentiment, purchasing power, fractional integration, long memory, unit root testing, inflation persistence, consumer confidence, University of Michigan Index of Consumer Sentiment, mean reversion, US macroeconomic time series, Discover Sustainability, time-series econometrics