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 7.76% per annum.
- LMT price at the close of May 16, 2024 was $464.83 and was higher than the top border of the primary price channel by $13.13 (2.91%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 53.16% per annum.
- LMT price at the close of May 16, 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 25, 2022
End date: March 26, 2024
a = 6.4557
b = -0.0002
s = 0.0306
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -7.76%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0306) – 1
= 13.01%
October 25, 2022 calculations
Top border of price channel:
Exp(Y867)
= Exp(a + b × X867 + 2 × s)
= Exp(a + b × 1,257 + 2 × s)
= Exp(6.4557 + -0.0002 × 1,257 + 2 × 0.0306)
= Exp(6.2389)
= $512.27
Bottom border of price channel:
Exp(Y867)
= Exp(a + b × X867 – 2 × s)
= Exp(a + b × 1,257 – 2 × s)
= Exp(6.4557 + -0.0002 × 1,257 – 2 × 0.0306)
= Exp(6.1165)
= $453.28
March 26, 2024 calculations
Top border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 + 2 × s)
= Exp(a + b × 1,775 + 2 × s)
= Exp(6.4557 + -0.0002 × 1,775 + 2 × 0.0306)
= Exp(6.1243)
= $456.82
Bottom border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 – 2 × s)
= Exp(a + b × 1,775 – 2 × s)
= Exp(6.4557 + -0.0002 × 1,775 – 2 × 0.0306)
= Exp(6.0020)
= $404.22
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 7.76% per annum.
- LMT price at the close of May 16, 2024 was $464.83 and was higher than the top border of the primary price channel by $13.13 (2.91%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 8, 2024
End date: May 14, 2024
a = 4.0244
b = 0.0012
s = 0.0082
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 53.16%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0082) – 1
= 3.32%
February 8, 2024 calculations
Top border of price channel:
Exp(Y1,190)
= Exp(a + b × X1,190 + 2 × s)
= Exp(a + b × 1,728 + 2 × s)
= Exp(4.0244 + 0.0012 × 1,728 + 2 × 0.0082)
= Exp(6.0590)
= $427.95
Bottom border of price channel:
Exp(Y1,190)
= Exp(a + b × X1,190 – 2 × s)
= Exp(a + b × 1,728 – 2 × s)
= Exp(4.0244 + 0.0012 × 1,728 – 2 × 0.0082)
= Exp(6.0263)
= $414.20
May 14, 2024 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.0244 + 0.0012 × 1,824 + 2 × 0.0082)
= Exp(6.1711)
= $478.73
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.0244 + 0.0012 × 1,824 – 2 × 0.0082)
= Exp(6.1385)
= $463.34
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 53.16% per annum.
- LMT price at the close of May 16, 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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