BUG: TimedeltaIndex.shift() infers freq when possible (GH#62094)

pandas/core/arrays/datetimelike.py

@@ -1070,26 +1070,13 @@ def _get_arithmetic_result_freq(self, other) -> BaseOffset | None:
         elif isinstance(self.freq, Tick):
             # In these cases
             return self.freq
-        elif self.dtype.kind == "m" and isinstance(other, Timedelta):
-            return self.freq
-        elif (
-            self.dtype.kind == "m"
-            and isinstance(other, Timestamp)
-            and (other.tz is None or timezones.is_utc(other.tz))
-        ):
-            # e.g. test_td64arr_add_sub_datetimelike_scalar tdarr + timestamp
-            #  gives a DatetimeArray. As long as the timestamp has no timezone
-            #  or UTC, the result can retain a Day freq.
-            return self.freq
-        elif (
-            lib.is_np_dtype(self.dtype, "M")
-            and isinstance(self.freq, Day)
-            and isinstance(other, Timedelta)
-        ):
-            # e.g. TestTimedelta64ArithmeticUnsorted::test_timedelta
-            # Day is unambiguously 24h
-            return self.freq
-
+        # If no explicit freq, use inferred_freq when the index is regular
+        elif self.freq is None:
+            inferred = self.inferred_freq
+            if inferred is not None:
+                offset = to_offset(inferred)
+                if isinstance(offset, Tick):
+                    return offset
         return None
 
     @final

pandas/tests/indexes/timedeltas/test_arithmetic.py

@@ -2,6 +2,7 @@
 # Other cases can be shared in tests.arithmetic.test_timedelta64
 import numpy as np
 
+import pandas as pd
 from pandas import (
     NaT,
     Timedelta,
@@ -49,3 +50,11 @@ def test_tdi_division(self, index_or_series):
             [31 * 86400, 31 * 86400, 31 * 86400 + 5 * 60 + 3, np.nan]
         )
         tm.assert_equal(result, expected)
+
+    def test_timedeltaindex_shift_infers_freq(self):
+        # GH#62094: TimedeltaIndex.shift() should work if freq can be inferred
+        ind = pd.date_range("1/1/2021", "1/5/2021") - pd.Timestamp("1/3/2019")
+        shifted = ind.shift(1)
+        expected = ind + Timedelta(days=1)
+        tm.assert_index_equal(shifted, expected)
+        assert shifted.freq == pd.tseries.frequencies.to_offset("D")