Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 129.21% per annum.
- TGT price at the close of February 28, 2025 was $124.24 and was lower than the bottom border of the primary price channel by $4,308.53 (97.20%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 12.53% per annum.
- TGT price at the close of February 28, 2025 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 TGT 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: April 1, 2021
End date: August 16, 2021
a = 4.2870
b = 0.0023
s = 0.0176
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0023) – 1
= 129.21%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0176) – 1
= 7.29%
April 1, 2021 calculations
Top border of price channel:
Exp(Y274)
= Exp(a + b × X274 + 2 × s)
= Exp(a + b × 395 + 2 × s)
= Exp(4.2870 + 0.0023 × 395 + 2 × 0.0176)
= Exp(5.2197)
= $184.89
Bottom border of price channel:
Exp(Y274)
= Exp(a + b × X274 – 2 × s)
= Exp(a + b × 395 – 2 × s)
= Exp(4.2870 + 0.0023 × 395 – 2 × 0.0176)
= Exp(5.1494)
= $172.33
August 16, 2021 calculations
Top border of price channel:
Exp(Y368)
= Exp(a + b × X368 + 2 × s)
= Exp(a + b × 532 + 2 × s)
= Exp(4.2870 + 0.0023 × 532 + 2 × 0.0176)
= Exp(5.5311)
= $252.41
Bottom border of price channel:
Exp(Y368)
= Exp(a + b × X368 – 2 × s)
= Exp(a + b × 532 – 2 × s)
= Exp(4.2870 + 0.0023 × 532 – 2 × 0.0176)
= Exp(5.4607)
= $235.27
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 129.21% per annum.
- TGT price at the close of February 28, 2025 was $124.24 and was lower than the bottom border of the primary price channel by $4,308.53 (97.20%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 1, 2021
End date: February 28, 2025
a = 5.4650
b = -0.0004
s = 0.1492
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -12.53%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1492) – 1
= 81.65%
April 1, 2021 calculations
Top border of price channel:
Exp(Y274)
= Exp(a + b × X274 + 2 × s)
= Exp(a + b × 395 + 2 × s)
= Exp(5.4650 + -0.0004 × 395 + 2 × 0.1492)
= Exp(5.6186)
= $275.49
Bottom border of price channel:
Exp(Y274)
= Exp(a + b × X274 – 2 × s)
= Exp(a + b × 395 – 2 × s)
= Exp(5.4650 + -0.0004 × 395 – 2 × 0.1492)
= Exp(5.0216)
= $151.66
February 28, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.4650 + -0.0004 × 1,824 + 2 × 0.1492)
= Exp(5.0944)
= $163.11
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.4650 + -0.0004 × 1,824 – 2 × 0.1492)
= Exp(4.4975)
= $89.79
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 12.53% per annum.
- TGT price at the close of February 28, 2025 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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