diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index bf14ed44e3a1c..48f62fe888b9a 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -463,7 +463,7 @@ def astype(self, dtype: Dtype, copy: bool = True) -> ArrayLike:
                 return self
             return self._set_dtype(dtype)
         if is_extension_array_dtype(dtype):
-            return array(self, dtype=dtype, copy=copy)  # type: ignore # GH 28770
+            return array(self, dtype=dtype, copy=copy)
         if is_integer_dtype(dtype) and self.isna().any():
             raise ValueError("Cannot convert float NaN to integer")
         return np.array(self, dtype=dtype, copy=copy)
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 407daf15d5cce..76788f3f97a28 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1,6 +1,6 @@
 from datetime import datetime, timedelta
 import operator
-from typing import Any, Sequence, Type, Union, cast
+from typing import Any, Sequence, Type, TypeVar, Union, cast
 import warnings
 
 import numpy as np
@@ -437,6 +437,9 @@ def _with_freq(self, freq):
         return self
 
 
+DatetimeLikeArrayT = TypeVar("DatetimeLikeArrayT", bound="DatetimeLikeArrayMixin")
+
+
 class DatetimeLikeArrayMixin(
     ExtensionOpsMixin, AttributesMixin, NDArrayBackedExtensionArray
 ):
@@ -679,7 +682,7 @@ def _concat_same_type(cls, to_concat, axis: int = 0):
 
         return cls._simple_new(values, dtype=dtype, freq=new_freq)
 
-    def copy(self):
+    def copy(self: DatetimeLikeArrayT) -> DatetimeLikeArrayT:
         values = self.asi8.copy()
         return type(self)._simple_new(values, dtype=self.dtype, freq=self.freq)
 
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index 2d9522b00627c..b7dfcd4cb188c 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -1,6 +1,6 @@
 from datetime import timedelta
 import operator
-from typing import Any, Callable, List, Optional, Sequence, Union
+from typing import Any, Callable, List, Optional, Sequence, Type, Union
 
 import numpy as np
 
@@ -20,6 +20,7 @@
     period_asfreq_arr,
 )
 from pandas._libs.tslibs.timedeltas import Timedelta, delta_to_nanoseconds
+from pandas._typing import AnyArrayLike
 from pandas.util._decorators import cache_readonly
 
 from pandas.core.dtypes.common import (
@@ -172,8 +173,8 @@ def _simple_new(cls, values: np.ndarray, freq=None, **kwargs) -> "PeriodArray":
 
     @classmethod
     def _from_sequence(
-        cls,
-        scalars: Sequence[Optional[Period]],
+        cls: Type["PeriodArray"],
+        scalars: Union[Sequence[Optional[Period]], AnyArrayLike],
         dtype: Optional[PeriodDtype] = None,
         copy: bool = False,
     ) -> "PeriodArray":
@@ -186,7 +187,6 @@ def _from_sequence(
             validate_dtype_freq(scalars.dtype, freq)
             if copy:
                 scalars = scalars.copy()
-            assert isinstance(scalars, PeriodArray)  # for mypy
             return scalars
 
         periods = np.asarray(scalars, dtype=object)
@@ -772,7 +772,7 @@ def raise_on_incompatible(left, right):
 
 
 def period_array(
-    data: Sequence[Optional[Period]],
+    data: Union[Sequence[Optional[Period]], AnyArrayLike],
     freq: Optional[Union[str, Tick]] = None,
     copy: bool = False,
 ) -> PeriodArray:
diff --git a/pandas/core/construction.py b/pandas/core/construction.py
index 2f71f4f4ccc19..351ef1d0429da 100644
--- a/pandas/core/construction.py
+++ b/pandas/core/construction.py
@@ -13,7 +13,7 @@
 
 from pandas._libs import lib
 from pandas._libs.tslibs import IncompatibleFrequency, OutOfBoundsDatetime
-from pandas._typing import ArrayLike, Dtype, DtypeObj
+from pandas._typing import AnyArrayLike, ArrayLike, Dtype, DtypeObj
 
 from pandas.core.dtypes.cast import (
     construct_1d_arraylike_from_scalar,
@@ -54,7 +54,9 @@
 
 
 def array(
-    data: Sequence[object], dtype: Optional[Dtype] = None, copy: bool = True,
+    data: Union[Sequence[object], AnyArrayLike],
+    dtype: Optional[Dtype] = None,
+    copy: bool = True,
 ) -> "ExtensionArray":
     """
     Create an array.