Reject an ARIMA period too short for its own orders

Indicators/AutoRegressiveIntegratedMovingAverage.cs

@@ -131,9 +131,14 @@ public AutoRegressiveIntegratedMovingAverage(
                     "currently available fitting methods.");
             }
 
-            if (period < Math.Max(arOrder, maOrder))
+            // ComputeNextValue indexes arrayData and _residuals up to 2 * maOrder, over a
+            // series DifferenceSeries shortens only when diffOrder is positive.
+            var shortest = Math.Max(arOrder, maOrder > 0 ? (2 * maOrder) + 1 : 0)
+                + Math.Max(diffOrder, 0);
+            if (period < shortest)
             {
-                throw new ArgumentException("Period must exceed both arOrder and maOrder");
+                throw new ArgumentException($"Period parameter for ARIMA({arOrder}, {diffOrder}, " +
+                    $"{maOrder}) indicator must be at least {shortest} but was {period}");
             }
 
             _arOrder = arOrder;

Tests/Indicators/AutoregressiveIntegratedMovingAverageTests.cs

@@ -69,6 +69,31 @@ public void AcceptsAnAutoRegressiveOrderAboveTheMovingAverageOrder(int arOrder,
             Assert.IsTrue(arima.IsReady);
         }
 
+        [TestCase(1, 0, 1, 3)]
+        [TestCase(1, 1, 1, 4)]
+        [TestCase(2, 1, 2, 6)]
+        [TestCase(1, 2, 0, 3)]
+        [TestCase(1, -2, 1, 3)]
+        [TestCase(1, -3, 2, 5)]
+        public void RejectsAPeriodTooShortForItsOrders(int arOrder, int diffOrder, int maOrder, int shortest)
+        {
+            var exception = Assert.Throws<ArgumentException>(() =>
+                new AutoRegressiveIntegratedMovingAverage(arOrder, diffOrder, maOrder, shortest - 1, true));
+            Assert.That(exception.Message, Is.EqualTo(
+                $"Period parameter for ARIMA({arOrder}, {diffOrder}, {maOrder}) indicator " +
+                $"must be at least {shortest} but was {shortest - 1}"));
+
+            var arima = new AutoRegressiveIntegratedMovingAverage(arOrder, diffOrder, maOrder, shortest, true);
+            var reference = new DateTime(2020, 1, 1);
+
+            for (var i = 0; i < shortest + 1; i++)
+            {
+                arima.Update(reference.AddDays(i), 100m + (decimal)Math.Sin(i / 3d) * 5m);
+            }
+
+            Assert.IsTrue(arima.IsReady);
+        }
+
         [Test]
         public void PredictionErrorAgainstExternalData()
         {