diff --git a/doc/source/whatsnew/v0.17.0.txt b/doc/source/whatsnew/v0.17.0.txt
index f88e5c0a11f9f..b861bf51b80eb 100644
--- a/doc/source/whatsnew/v0.17.0.txt
+++ b/doc/source/whatsnew/v0.17.0.txt
@@ -1009,4 +1009,6 @@ Bug Fixes
 - Bug in ``.var()`` causing roundoff errors for highly similar values (:issue:`10242`)
 - Bug in ``DataFrame.plot(subplots=True)`` with duplicated columns outputs incorrect result (:issue:`10962`)
 - Bug in ``Index`` arithmetic may result in incorrect class (:issue:`10638`)
+- Bug in ``date_range`` results in empty if freq is negative annualy, quarterly and monthly (:issue:`11018`)
+- Bug in ``DatetimeIndex`` cannot infer negative freq (:issue:`11018`)
 
diff --git a/pandas/tests/test_index.py b/pandas/tests/test_index.py
index 36bc0755f9a6a..1ec73edbb82e5 100644
--- a/pandas/tests/test_index.py
+++ b/pandas/tests/test_index.py
@@ -3329,7 +3329,7 @@ def test_ufunc_coercions(self):
             exp = TimedeltaIndex(['-2H', '-4H', '-6H', '-8H', '-10H'],
                                  freq='-2H', name='x')
             tm.assert_index_equal(result, exp)
-            self.assertEqual(result.freq, None)
+            self.assertEqual(result.freq, '-2H')
 
         idx = TimedeltaIndex(['-2H', '-1H', '0H', '1H', '2H'],
                                 freq='H', name='x')
diff --git a/pandas/tseries/frequencies.py b/pandas/tseries/frequencies.py
index d7eaab5a5a186..6a4257d101473 100644
--- a/pandas/tseries/frequencies.py
+++ b/pandas/tseries/frequencies.py
@@ -887,7 +887,8 @@ def __init__(self, index, warn=True):
         if len(index) < 3:
             raise ValueError('Need at least 3 dates to infer frequency')
 
-        self.is_monotonic = self.index.is_monotonic
+        self.is_monotonic = (self.index.is_monotonic_increasing or
+                             self.index.is_monotonic_decreasing)
 
     @cache_readonly
     def deltas(self):
@@ -971,7 +972,6 @@ def month_position_check(self):
 
         from calendar import monthrange
         for y, m, d, wd in zip(years, months, days, weekdays):
-            wd = datetime(y, m, d).weekday()
 
             if calendar_start:
                 calendar_start &= d == 1
@@ -1025,7 +1025,7 @@ def _infer_daily_rule(self):
 
         monthly_rule = self._get_monthly_rule()
         if monthly_rule:
-            return monthly_rule
+            return _maybe_add_count(monthly_rule, self.mdiffs[0])
 
         if self.is_unique:
             days = self.deltas[0] / _ONE_DAY
@@ -1111,7 +1111,7 @@ def _infer_daily_rule(self):
 
 
 def _maybe_add_count(base, count):
-    if count > 1:
+    if count != 1:
         return '%d%s' % (count, base)
     else:
         return base
diff --git a/pandas/tseries/offsets.py b/pandas/tseries/offsets.py
index fb6929c77f6b0..e15be45ef305a 100644
--- a/pandas/tseries/offsets.py
+++ b/pandas/tseries/offsets.py
@@ -2615,15 +2615,24 @@ def generate_range(start=None, end=None, periods=None,
         start = end - (periods - 1) * offset
 
     cur = start
-
-    while cur <= end:
-        yield cur
-
-        # faster than cur + offset
-        next_date = offset.apply(cur)
-        if next_date <= cur:
-            raise ValueError('Offset %s did not increment date' % offset)
-        cur = next_date
+    if offset.n >= 0:
+        while cur <= end:
+            yield cur
+
+            # faster than cur + offset
+            next_date = offset.apply(cur)
+            if next_date <= cur:
+                raise ValueError('Offset %s did not increment date' % offset)
+            cur = next_date
+    else:
+        while cur >= end:
+            yield cur
+
+            # faster than cur + offset
+            next_date = offset.apply(cur)
+            if next_date >= cur:
+                raise ValueError('Offset %s did not decrement date' % offset)
+            cur = next_date
 
 prefix_mapping = dict((offset._prefix, offset) for offset in [
     YearBegin,                # 'AS'
diff --git a/pandas/tseries/tests/test_base.py b/pandas/tseries/tests/test_base.py
index 4a72b094917b5..24edc54582ec1 100644
--- a/pandas/tseries/tests/test_base.py
+++ b/pandas/tseries/tests/test_base.py
@@ -494,6 +494,15 @@ def test_take(self):
             self.assert_index_equal(result, expected)
             self.assertIsNone(result.freq)
 
+    def test_infer_freq(self):
+        # GH 11018
+        for freq in ['A', '2A', '-2A', 'Q', '-1Q', 'M', '-1M', 'D', '3D', '-3D',
+                     'W', '-1W', 'H', '2H', '-2H', 'T', '2T', 'S', '-3S']:
+            idx = pd.date_range('2011-01-01 09:00:00', freq=freq, periods=10)
+            result = pd.DatetimeIndex(idx.asi8, freq='infer')
+            tm.assert_index_equal(idx, result)
+            self.assertEqual(result.freq, freq)
+
 
 class TestTimedeltaIndexOps(Ops):
 
@@ -1108,6 +1117,14 @@ def test_take(self):
             self.assert_index_equal(result, expected)
             self.assertIsNone(result.freq)
 
+    def test_infer_freq(self):
+        # GH 11018
+        for freq in ['D', '3D', '-3D', 'H', '2H', '-2H', 'T', '2T', 'S', '-3S']:
+            idx = pd.timedelta_range('1', freq=freq, periods=10)
+            result = pd.TimedeltaIndex(idx.asi8, freq='infer')
+            tm.assert_index_equal(idx, result)
+            self.assertEqual(result.freq, freq)
+
 
 class TestPeriodIndexOps(Ops):
 
diff --git a/pandas/tseries/tests/test_frequencies.py b/pandas/tseries/tests/test_frequencies.py
index a642c12786940..d9bc64136e390 100644
--- a/pandas/tseries/tests/test_frequencies.py
+++ b/pandas/tseries/tests/test_frequencies.py
@@ -539,7 +539,7 @@ def test_infer_freq_businesshour(self):
     def test_not_monotonic(self):
         rng = _dti(['1/31/2000', '1/31/2001', '1/31/2002'])
         rng = rng[::-1]
-        self.assertIsNone(rng.inferred_freq)
+        self.assertEqual(rng.inferred_freq, '-1A-JAN')
 
     def test_non_datetimeindex(self):
         rng = _dti(['1/31/2000', '1/31/2001', '1/31/2002'])
diff --git a/pandas/tseries/tests/test_timedeltas.py b/pandas/tseries/tests/test_timedeltas.py
index d3d09356648b0..69dc70698ca28 100644
--- a/pandas/tseries/tests/test_timedeltas.py
+++ b/pandas/tseries/tests/test_timedeltas.py
@@ -1539,8 +1539,7 @@ def test_tdi_ops_attributes(self):
         result = - rng
         exp = timedelta_range('-2 days', periods=5, freq='-2D', name='x')
         tm.assert_index_equal(result, exp)
-        # tdi doesn't infer negative freq
-        self.assertEqual(result.freq, None)
+        self.assertEqual(result.freq, '-2D')
 
         rng = pd.timedelta_range('-2 days', periods=5, freq='D', name='x')
 
@@ -1548,7 +1547,6 @@ def test_tdi_ops_attributes(self):
         exp = TimedeltaIndex(['2 days', '1 days', '0 days', '1 days',
                               '2 days'], name='x')
         tm.assert_index_equal(result, exp)
-        # tdi doesn't infer negative freq
         self.assertEqual(result.freq, None)
 
 
diff --git a/pandas/tseries/tests/test_timeseries.py b/pandas/tseries/tests/test_timeseries.py
index a021195ea6c04..565ce43dc46a1 100644
--- a/pandas/tseries/tests/test_timeseries.py
+++ b/pandas/tseries/tests/test_timeseries.py
@@ -1260,6 +1260,18 @@ def test_date_range_gen_error(self):
         rng = date_range('1/1/2000 00:00', '1/1/2000 00:18', freq='5min')
         self.assertEqual(len(rng), 4)
 
+    def test_date_range_negative_freq(self):
+        # GH 11018
+        rng = date_range('2011-12-31', freq='-2A', periods=3)
+        exp = pd.DatetimeIndex(['2011-12-31', '2009-12-31', '2007-12-31'], freq='-2A')
+        self.assert_index_equal(rng, exp)
+        self.assertEqual(rng.freq, '-2A')
+
+        rng = date_range('2011-01-31', freq='-2M', periods=3)
+        exp = pd.DatetimeIndex(['2011-01-31', '2010-11-30', '2010-09-30'], freq='-2M')
+        self.assert_index_equal(rng, exp)
+        self.assertEqual(rng.freq, '-2M')
+
     def test_first_subset(self):
         ts = _simple_ts('1/1/2000', '1/1/2010', freq='12h')
         result = ts.first('10d')