Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 7.81% per annum.
- LMT price at the close of April 24, 2024 was $459.14 and was higher than the top border of the primary price channel by $5.43 (1.20%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 58.82% per annum.
- LMT price at the close of April 24, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of LMT price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: October 26, 2022
End date: March 26, 2024
a = 6.4630
b = -0.0002
s = 0.0305
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -7.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0305) – 1
= 12.99%
October 26, 2022 calculations
Top border of price channel:
Exp(Y884)
= Exp(a + b × X884 + 2 × s)
= Exp(a + b × 1,280 + 2 × s)
= Exp(6.4630 + -0.0002 × 1,280 + 2 × 0.0305)
= Exp(6.2390)
= $512.37
Bottom border of price channel:
Exp(Y884)
= Exp(a + b × X884 – 2 × s)
= Exp(a + b × 1,280 – 2 × s)
= Exp(6.4630 + -0.0002 × 1,280 – 2 × 0.0305)
= Exp(6.1169)
= $453.47
March 26, 2024 calculations
Top border of price channel:
Exp(Y1,238)
= Exp(a + b × X1,238 + 2 × s)
= Exp(a + b × 1,797 + 2 × s)
= Exp(6.4630 + -0.0002 × 1,797 + 2 × 0.0305)
= Exp(6.1239)
= $456.65
Bottom border of price channel:
Exp(Y1,238)
= Exp(a + b × X1,238 – 2 × s)
= Exp(a + b × 1,797 – 2 × s)
= Exp(6.4630 + -0.0002 × 1,797 – 2 × 0.0305)
= Exp(6.0018)
= $404.16
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 7.81% per annum.
- LMT price at the close of April 24, 2024 was $459.14 and was higher than the top border of the primary price channel by $5.43 (1.20%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 13, 2024
End date: April 24, 2024
a = 3.8202
b = 0.0013
s = 0.0082
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 58.82%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0082) – 1
= 3.32%
February 13, 2024 calculations
Top border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 + 2 × s)
= Exp(a + b × 1,755 + 2 × s)
= Exp(3.8202 + 0.0013 × 1,755 + 2 × 0.0082)
= Exp(6.0608)
= $428.70
Bottom border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 – 2 × s)
= Exp(a + b × 1,755 – 2 × s)
= Exp(3.8202 + 0.0013 × 1,755 – 2 × 0.0082)
= Exp(6.0281)
= $414.91
April 24, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.8202 + 0.0013 × 1,826 + 2 × 0.0082)
= Exp(6.1507)
= $469.07
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.8202 + 0.0013 × 1,826 – 2 × 0.0082)
= Exp(6.1180)
= $453.98
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 58.82% per annum.
- LMT price at the close of April 24, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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